This has been CNBC's live blog covering updates on the war in Ukraine. [Follow the latest updates here.]

The World Bank has lowered its annual global growth forecast for 2022 by nearly a full percentage point, from 4.1% down to 3.2%, citing the pressure that Russia's invasion of Ukraine has placed on the global economy.

The Ukrainian military says Russia's long-expected offensive push into eastern Ukraine has started, with intensified assaults Monday in the Slobozhansky and Donetsk operational districts in the north and east of the country.

Increased attacks were also recorded near the cities of Izyum in the Kharkiv district and Sloviansk in the Donetsk district, as well as around Severodonetsk and Popasna in the Luhansk region, farther east.

Meanwhile, the U.S. has flown four military cargo aircraft of security assistance into the region in the last 24 hours, with another flight into the theater expected before Tuesday afternoon, a defense official said.

The weapons are part of President Joe Biden's $800 million assistance package announced last week, a package that includes heavy artillery directly from the stockpiles of the U.S. Army and Marine Corps.

American military specialists will begin training Ukrainian troops on how to operate the howitzer artillery systems in "the next several days," Pentagon spokesman John Kirby said during a daily briefing.

Zelenskyy: 'Very large part' of Russian army now focused on the east

Russia has begun the battle for Donbas, Ukrainian President Volodymyr Zelenskyy said in his nightly video address to the nation.

"A very large part of the entire Russian army is now focused on this offensive," he said.

He also said that Russian forces were increasing pressure in some other regions, with continued rocket strikes.

"Today's strikes at Lviv, at the Dnipropetrovsk region and any other Russian strikes mean only one thing: we, the world and history will take from Russia much more than Russian missiles will take from Ukraine," he said.

He added that the none of the missile strikes have changed the situation for Russia "tangibly."

Zelenskyy also said that Ukraine's accession to the European Union is an "integral" part of post-war reconstruction and the country's future development.

"The status of a candidate for membership in the European Union will open for us unprecedented opportunities in our history for the restoration and modernization of Ukraine," he said.

— Chelsea Ong

U.S. still sees no indications China is helping Russia wage its war in Ukraine

The United States has yet to see any evidence that China is providing material support to Russia in its ongoing war in Ukraine, State Department spokesman Ned Price said.

Nonetheless, U.S. officials continue to watch for indications that Beijing is helping Moscow in any way, including with sanctions evasion.

"The PRC is going to make its own decisions about how it supports Russia's brutality against the people of Ukraine," Price said at a daily briefing, using an abbreviation of the People's Republic of China.

He called on Beijing to "make clear where it stands" on Russia's unprovoked war in Ukraine.

"Of course, if the PRC were to provide weapons, supplies or seek to help Russia evade sanctions, there would be strong consequences for that," said Price.

Neither the State Department nor the White House has detailed exactly what the consequences would be for China if it were found to be helping Moscow prosecute its brutal campaign against both Ukrainian soldiers and increasingly, civilians.

In the weeks since Russia's invasion of its ex-Soviet neighbor, Washington and its allies have imposed a half dozen rounds of coordinated sanctions on Russia, quickly transforming the one-time G-8 member into the world's most-sanctioned nation.

Last week, national security advisor Jake Sullivan admitted that while the U.S. is closely tracking the trade between Russia and China, it's impossible to know exactly what's passing between the two allies 24-7.

"It's something that we constantly monitor, and of course we don't have complete visibility all the time," Sullivan told The Economic Club of Washington.

"Russia and China have an economic relationship, and there is continuing economic intercourse between Russia and China," said Sullivan.

"But have we seen a systematic effort to undermine, weaken or defy sanctions at this point? We have not."

— Amanda Macias

Russia's planned offensive in eastern Ukraine has begun, Kyiv officials say

The Ukrainian military says Russia's long-expected offensive push into eastern Ukraine has started, with intensified assaults Monday in the Slobozhansky and Donetsk operational districts in the north and east of the country.

Increased attacks were also recorded near the cities of Izyum in the Kharkiv district and Sloviansk in the Donetsk district, as well as around Severodonetsk and Popasna in the Luhansk region, farthest east.

Earlier on Monday, a senior U.S. Defense official told reporters on a conference call that 11 additional Russian battalion tactical groups moved into Ukraine over the weekend, bringing the total number of BTGs up to 76. The official added that the majority of Russia's ground forces have repositioned in eastern and southern Ukraine.

Russia is expected to deploy the additional troops in part to support the fighting of the main forces and to protect administrative buildings and infrastructure in Kremlin-occupied territories, said Oleksandr Shtupun, a spokesman for the General Staff of the Ukrainian armed forces.

The attacks mark the start of what many analysts and combatants on both sides believe will be the most brutal chapter in Russia's nearly two-month campaign to seize control of Ukraine and its 44 million citizens.

That effort that has so far failed, and the shift underway to concentrate firepower in areas of Ukraine that are already under Russian control is widely viewed as a way for Russian President Vladimir Putin to extract a smaller victory from the Kremlin's large-scale defeat.

— Christina Wilkie

U.S. to train Ukrainian troops on heavy artillery systems in the 'next several days,' Pentagon says

The U.S. military will begin training Ukrainian troops on how to operate American howitzer artillery systems in "the next several days," Pentagon spokesman John Kirby said during a daily briefing.

"I'm not going to get into locations, they will be outside of Ukraine," Kirby said. He also declined to say "who is going to be doing the training and what timeline," citing the need to protect operational security.

Following weeks of pressure from Kyiv to supply its forces with heavy artillery in advance of an expected full-scale Russian assault in the east, Kirby confirmed Monday that the Pentagon has provided 18 howitzers to Ukraine.

"It's important to remember this particular system is newer to Ukrainians, they don't use U.S. howitzers but they know how to use artillery," he said, adding that the Pentagon did not believe it would take long to "get them up to speed."

Earlier on Monday, a senior U.S. Defense official told reporters on a conference call that the howitzers deployed to Ukraine are coming from both Army and Marine Corps stockpiles.

— Amanda Macias

Sanctions cripple Russia's defense industry as U.S. sends more firepower to Ukraine

A senior U.S. Defense official said the punishing rounds of U.S. and European sanctions on Russia are beginning to have an impact on Moscow's ability to finance its war in Ukraine.

The official, who declined to be named in order to share new details from the Pentagon's ongoing assessment of the war, told reporters on a conference call that the sanctions have greatly limited Russia's ability to resupply stocks of its precision-guided munitions because of a lack of components. The official said that the Western sanctions have also limited Russia's overall defense production.

Meanwhile, the U.S. has flown four military cargo aircraft of security assistance into the region in the last 24 hours. The official said that another flight into the theater is expected within the next 24 hours. The official declined to detail the weapons on the aircraft citing operation security concerns but said that the security assistance is part of President Joe Biden's $800 million assistance package announced last week.

— Amanda Macias

Russia expands its military footprint in Ukraine as Mariupol takes brunt of strikes

A senior U.S. Defense official says that Russian forces have added to their footprint inside of Ukraine, with nearly all of their ground forces deployed to eastern and southern parts of the country.

The official, who spoke on the condition of anonymity, said that the Kremlin added at least 11 battalion tactical groups into Ukraine over the weekend, bringing the force up to 76 separate groups. The official would not specify exactly how many troops were in each battalion group, but they traditionally comprise between 600-800 soldiers.

The Defense official said that the U.S. has also observed Russia move other military enablers, including command and control and artillery specialists into Ukraine's Donbas region.

The Kremlin is expected to launch a major offensive there in the near future, part of the Russian military's shift in focus after weeks of failed advances on Kyiv.

The official said that the coastal city of Mariupol is bearing the brunt of Russian airstrikes and artillery bombardment.

"We did see some strikes in Kyiv and Lviv in the last 24 hours or so, but they were by exception," the official said, adding that the U.S. has observed about 200 sorties.

— Amanda Macias

Latest UN figures show 2,072 civilians killed and 2,818 injured in Ukraine

The United Nations says it has confirmed 2,072 civilian deaths and 2,818 injuries in Ukraine since Russia invaded its ex-Soviet neighbor on Feb. 24.

Of those killed, the U.N. has identified at least 38 girls and 60 boys, as well as 71 children whose gender is unknown.

The Office of the UN High Commissioner for Human Rights said Monday that the death toll in Ukraine is likely higher, citing delayed reporting due to the armed conflict.

The international body said most of the civilian casualties recorded were caused by the use of explosive weapons, including shelling from heavy artillery and multiple launch rocket systems, as well as missiles and airstrikes.

— Amanda Macias

Putin says the West's 'economic blitz' against Russia has failed

Russian President Vladimir Putin says that the barrage of Western sanctions against Russia has failed to accomplish its goal of derailing Russia's economy.

Putin said Monday that the West "expected to quickly upset the financial-economic situation, provoke panic in the markets, the collapse of the banking system and shortages in stores." He added that "the strategy of the economic blitz has failed."

The Russian leader spoke in televised remarks during a video call with top economic officials.

Putin noted that "Russia has withstood the unprecedented pressure," arguing that the ruble has strengthened and the country has recorded a historic high trade surplus of $58 billion in the first quarter of the year.

Instead, Putin contended that the sanctions backfired against the U.S. and its European allies, speeding up inflation and leading to a drop in living standards.

Putin acknowledged a sharp hike in consumer prices in Russia, saying they rose by 17.5% as of April on a year-to-year basis and directing the government to index wages and other payments to alleviate the impact of inflation on people's incomes.

— Associated Press

World Bank cuts global growth forecast to 3.2% from 4.1%, citing Ukraine war

The World Bank has lowered its annual global growth forecast for 2022 by nearly a full percentage point, from 4.1% down to 3.2%, citing the pressure that Russia's invasion of Ukraine has placed on the global economy.

World Bank President David Malpass told reporters on a conference call that the largest single factor in the reduced growth forecast was a projected economic contraction of 4.1% across Europe and Central Asia, according to Reuters.

Other factors driving the growth cut include higher prices that developed countries across the world are paying for food and fuel, partly as a result of Western sanctions on Russian energy and supply disruptions of Ukrainian and Russian agricultural products.

In order to help mitigate the shortages, Malpass said the World Bank was setting a new crisis financing target of $170 billion over the next 15 months.

--- Christina Wilkie

Zelenskyy discusses Ukraine's post-war reconstruction with IMF chief

Zelenskyy spoke with the head of the International Monetary Fund, discussing prospects for financial recovery and reconstruction in what he described as a positive conversation.

"Discussed with IMF Managing Director Georgieva the issue of ensuring Ukraine's financial stability & preparations for post-war reconstruction. We have clear plans for now, as well as a vision of prospects. I'm sure cooperation between the IMF & Ukraine will continue to be fruitful," Zelenskyy wrote in a tweet.

In a reply, Kristalina Georgieva tweeted, "Thank you @ZelenskyyUA for the very good call today. Continued economic support by Ukraine's partners is essential to lay the foundations for rebuilding a modern competitive #Ukraine."

Ukraine's economy is estimated to have been cut in half within a matter of weeks due to the Russian invasion. Ukrainian Prime Minister Denys Shmyhal has said he plans to seek more financial help for the country when he attends the IMF and World Bank meetings in Washington this week.

— Natasha Turak

'Street fights' in eastern town of Kreminna, Luhansk, as Russians troops launch offensive

Russian troops have entered the town of Kreminna in Ukraine's eastern Luhansk, one of the regions heavily bombarded by Russian forces and where officials expect to see far more intensified fighting in the coming days.

"The Russians entered Kreminna. Street fights began," said Serhii Haidai, head of the Luhansk regional military administration, in a Facebook post.

The offensive has begun, said, adding that the Russians entered Kreminna with "a huge amount of equipment."

Russian forces have been trying to push through Ukrainian resistance in Kreminna and other towns in the eastern Donetsk and Luhansk regions to take those territories, one of the key stated goals of the invasion.

— Natasha Turak

Lviv mayor accuses Kremlin of genocide, says no more 'safe' areas in Ukraine

The mayor of the western Ukrainian city of Lviv accused Moscow of carrying out a genocide after his city was hit with multiple Russian missiles that killed seven people and injured at least 11.

"What we see today is genocide. It's a deliberate action by the aggressor to kill peaceful civilians," Mayor Andriy Sadovyi said, adding: "All our cities and villages are in the same situation."

At least four Russian missiles struck Lviv early Monday morning, officials said, marking the first civilian deaths in the city since Russia began its invasion. Just 40 miles from the Polish border, Lviv has been seen as a safe haven for many Ukrainians fleeing shelling in the country's east.

Sadovyi said that children were among the injured, and that one of the missiles hit a garage and tire repair workshop, killing four people. He also said multiple windows were blown out, including in a school.

— Natasha Turak

Russian troops to close off entry and exit for besieged Mariupol

Russian troops have said they will close off Mariupol, preventing entry to and exit from the besieged eastern city and issuing "movement passes" to those who remain, an advisor to the mayor said.

Mariupol has been "wiped off the face of the earth," the governor of the Donetsk region said this week. The port city of originally some 500,000 people has suffered the highest volume of Russian bombardment since March 1, with the roughly 100,000 people left in the city cut off from electricity, water and humanitarian aid. Ukrainian officials estimate thousands of civilian deaths there.

Russia has demanded the city surrender, but Ukrainian forces have so far refused, despite heavy losses of both military personnel and civilians.

— Natasha Turak

Russia says it launched mass strikes on Ukrainian military targets overnight

Russia launched mass strikes to hit hundreds of Ukrainian military targets overnight, its defense ministry said in a statement.

It said that its air-launched missiles had destroyed 16 Ukrainian military facilities across the regions of Kharkiv, Zaporizhzhia, Donetsk and Dnipropetrovsk, as well as the port of Mykolayiv. The targets struck included five command posts, a fuel depot and three ammunition warehouses, as well as Ukrainian armor and forces, the statement said, adding that Russia's air force launched strikes on 108 areas where it said Ukrainian forces and weapons were concentrated.

The defense ministry also said that it used Iskander missiles to destroy four equipment and arms depots in Vinnytsia, Luhansk and Donetsk. NBC was not able to immediately verify the information.

— Natasha Turak

Four civilians shot dead while fleeing in Luhansk region: Governor

Four civilians were shot dead while trying to flee the town of Kreminna in Ukraine's eastern Luhansk region, regional governor Serhiy Gaidai said via the Telegram app.

They were trying to flee by car, he said, and were killed amid a Russian attack. He said that another person was seriously injured. NBC was not immediately able to verify the information.

Moscow claims it is only targeting military facilities in Ukraine and not civilians, despite abundant and well-documented evidence to the contrary.

— Natasha Turak

Five missile strikes hit Western city of Lviv, civilians killed, officials say

Air raid sirens are sounding once again in Ukraine's western city of Lviv after it was hit by five missile strikes, its mayor said. The strikes killed six people and wounded eight, according to the Lviv regional governor.

These are the first major strikes on Lviv in weeks, which until now was seen as a relatively safe haven for Ukrainians fleeing the country's embattled east. A mere 43 miles from the Polish border, Lviv is a key city connecting transport and shipment routes via rail — particularly, now, arms shipments from Poland.

— Natasha Turak

Mariupol resistance has slowed Russia's advance but at 'significant' human cost, UK says

Stubborn Ukrainian resistance in Mariupol has "severely tested Russian forces" and slowed Moscow's plans elsewhere, the British government said Monday. But the human cost has been "significant."

"Russian commanders will be concerned by the time it is taking to subdue Mariupol," the U.K. Ministry of Defence said in an intelligence update.

The Russian siege of Mariupol has come "at a significant cost to its residents," the ministry said. Much of the city has been destroyed, and the mayor of Mariupol said last week that 10,000 civilians have died there.

"The targeting of populated areas within Mariupol aligns with Russia's approach to Chechnya in 1999 and Syria in 2016," the ministry said.

Russia used artillery to almost entirely destroy the Chechen capital of Grozny in 1999, and Russia bombed civilian areas of Aleppo, Syria, from the air in 2016.

"This is despite the 24 February 2022 claims of Russia's Defence Ministry that Russia would neither strike cities nor threaten the Ukrainian population," the British government said.

A Russian embassy staff member has directed CNBC inquiries to the Russian Federation Ministry of Defense website, which is unavailable.

— Ted Kemp

Ukraine completes EU membership questionnaire

Ukraine has taken the first step in applying for membership to the European Union and completed a questionnaire to kick off the process, Reuters reported.

Ukrainian President Volodymyr Zelenskyy received the questionnaire and a promise for an accelerated application process from European Commission President Ursula von der Leyen when she visited Kyiv on April 8.

The commission now needs to evaluate Ukraine's ability to meet the necessary membership criteria.

The next scheduled European Council meeting is slated for June 23-24, where Ukraine expects to gain candidate country status.

— Chelsea Ong

Read CNBC's previous live coverage here:

Mariupol hasn’t surrendered to Russia, PM says; at least 5 dead, 20 injured in Kharkiv attack