Asia-Pacific markets are trading mixed; Taiwan market touches new highs

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 surged to record highs as it gained 0.46%, powered by technology and utility stocks.

Japan's Nikkei 225 extended gains to climb 0.42%, while the broad based Topix was 0.37% up.

South Korea's Kospi rebounded from Monday's losses, gaining 0.57%, while the small cap Kosdaq was 0.73% higher.

On the other hand, Hong Kong's Hang Seng index plunged 1.16% on its open, while the mainland Chinese CSI 300 index was 0.51% lower.

Australia's S&P/ASX 200 fell 1.27%.

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.