Japan's benchmark Nikkei 225 gained 0.3% to 21,170.63 in morning trading. Australia's S&P/ASX 200 lost 0.3% to 6,535.50, while South Korea's Kospi edged up nearly 0.2% to 2,099.26. Hong Kong's Hang Seng gained 1.2% to 27,447.42, while the Shanghai Composite was up 0.2% at 2,888.58.
On Wall Street, stocks ended a choppy week of trading with modest losses.
The S&P 500 index fell 4.66 points, or 0.2%, to 2,886.98 Friday and ended the week with a slim gain of 0.5%. The Dow Jones Industrial Average dropped 17.16 points, or 0.1%, to 26,089.61. The Nasdaq composite slid 40.47 points, or 0.5%, to 7,796.66. The Russell 2000 index of small company stocks dropped 13.30 points, or 0.9%, to 1,522.50.
Earlier this month, Federal Reserve Chair Jerome Powell set off a market rally after he signaled that the central bank is willing to cut interest rates to help stabilize the economy if the trade war between Washington and Beijing starts to slow economic growth.
The Fed holds its next meeting of policyholders this week, but no action on rates is expected.
Economists expect Fed officials to wait until the second week of July to indicate whether they intend to cut rates, after seeing the next government report on the jobs market and other economic data.
Market watchers are also closely watching the results of the G-20 summit in late June, where President Donald Trump and Chinese President Xi Jinping could meet and try to negotiate a deal on trade.
"Sentiments around the ability to achieve a positive turn in U.S.-China trade negotiations, should the Trump-Xi meeting materialize at the sidelines of the G-20, remain tentative," says Vishnu Varathan of Mizuho Bank in Singapore.
"And the G-20 itself is merely a stage to kick the can down the road and a long, long way off a complete retraction of global trade tensions."
Benchmark crude oil added 15 cents to $52.66 a barrel. It rose 0.4% to settle at $52.51 a barrel Friday. Brent crude oil, the international standard, added 29 cents to $62.30 a barrel.
The dollar rose to 108.57 Japanese yen from 108.23 yen on Friday. The euro weakened to $1.1222 from $1.1263.
AP Business Writer Damian J. Troise contributed to this report.
Copyright 2019 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.