Japan’s Nikkei 225 climbed 1.12% to come within 100 points of crossing the 39,000 mark for the first time in two weeks, while the broad-based Topix gained 0.65%.

In Australia, the S&P/ASX 200 inched up 0.12%, ahead of its trade data for April.

Futures for Hong Kong’s Hang Seng index stood at 18,396, pointing to a weaker open compared to the HSI’s close of 18,424.96.

South Korea’s markets were closed for a public holiday.

Overnight in the U.S., Nvidia led major tech stocks higher and slightly weak labor market data gave investors hope the Federal Reserve might move to lower interest rates later this year.

The S&P500 rose 1.18% to close at 5,354.03, a fresh record, and the Nasdaq Composite advanced 1.96% to 17,187.90, also a new record, as Nvidia shares jumped to make it the world’s second most valuable company.

The Dow Jones Industrial Average trailed a bit as stocks outside of technology underperformed, adding just 0.25%.

— CNBC’s Brian Evans and Alex Harring contributed to this report.