• Asia-Pacific markets like Australia, Hong Kong, mainland China and Taiwan returned to trade on Tuesday, after being closed for a public holiday the previous day.
• Traders in Asia will be looking to the U.S. Federal Reserve's decision on Wednesday stateside, which will come after the May inflation report is released the same day.

Asia-Pacific markets were mixed on Tuesday, even as the S&P 500 and Nasdaq Composite reached new highs on Wall Street overnight.

Traders in Asia will be looking to the U.S. Federal Reserve's decision on Wednesday stateside, which will come after the May inflation report is released earlier the same day.

Investors will parse through the Fed's updated projections on the timing and frequency of rate cuts. Markets are now pricing in just one rate cut this year, coming in November, according to the CME FedWatch Tool.

Asia-Pacific markets like Australia, Hong Kong, mainland China and Taiwan will return to trade on Tuesday, after being closed for a public holiday the previous day.

The Taiwan Weighted index reversed from a record high and fell 0.3%, ending at 21,792.12.

Japan's Nikkei 225 extended gains to climb 0.25% and close at 39,134.79, while the broad based Topix slipped 0.2% to 2,776.8.

South Korea's Kospi rebounded from Monday's losses, gaining 0.15% 2,705.32, while the small cap Kosdaq closed 0.42% higher at 868.36.

On the other hand, Hong Kong's Hang Seng index fell 0.88%, while the mainland Chinese CSI 300 index was 0.87% lower, hitting its lowest level in almost two months and closing at 3,542.88

Australia's S&P/ASX 200 fell 1.33%, ending the day at 7,755.4.

The broad S&P 500 index advanced by 0.26%, closing at 5,360.79, while the Nasdaq Composite gained 0.35% to end at 17,192.53.

The Dow Jones Industrial Average added 0.18%, tracking the rise in the S&P and Nasdaq.

— CNBC's Lisa Kailai Han and Sarah Min contributed to this report.