S&P and Nasdaq reach new records while Asia-Pacific markets trade with mixed results.

• Markets in Asia-Pacific countries, including Australia, Hong Kong, mainland China, and Taiwan, will resume trading on Tuesday following a public holiday closure the previous day.
• The U.S. Federal Reserve's decision on Wednesday, following the release of the May inflation report, will be closely watched by traders in Asia.

On Tuesday, Asia-Pacific markets opened with mixed results, while the Nasdaq Composite reached new heights on Wall Street overnight.

The U.S. Federal Reserve's decision on Wednesday, following the release of the May inflation report, will be closely watched by traders in Asia.

The Fed's updated projections on the timing and frequency of rate cuts will be scrutinized by investors. Currently, markets anticipate only one rate cut this year, which is scheduled for November, as indicated by the CME FedWatch Tool.

Markets in Asia-Pacific countries, including Australia, Hong Kong, mainland China, and Taiwan, will resume trading on Tuesday following a public holiday closure the previous day.

Japan's stock market gained 0.42%, while the broad-based Topix index rose by 0.34%.

On Monday, South Korea's stock market rebounded, gaining 0.4%, while the small cap Kosdaq rose by 0.64%.

Australia's S&P/ASX 200 fell 1%.

The Hang Seng index futures in Hong Kong were lower than the HSI's last close, at 18,096 compared to 18,366.95.

The S&P 500 index increased by 0.26% to finish at 5,360.79, while the Nasdaq Composite rose by 0.35% to end at 17,192.53.

The S&P and Nasdaq rose, causing the Dow Jones Industrial Average to increase by 0.18%.

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