Japan's benchmark Nikkei 225 rose 0.3% to 21,204.28. Australia's S&P/ASX 200 added 1.6% to 6,546.30. South Korea's Kospi gained 0.7% to 2,114.39. Hong Kong's Hang Seng stood at 27,851.68, up nearly 1.0%, while the Shanghai Composite edged up 2.5% at 2,922.00.
On Wall Street, shares continued their winning streak for a fifth day on Monday. That follows the strongest week for stocks since November in what has been a marked turnaround for the market after escalating trade tensions fueled a turbulent skid in May.
During an interview with CNBC, Trump said he expects to meet with Chinese President Xi Jinping at the Group of 20 summit in Japan later this month. That may have given investors some cause for optimism in the dispute between Washington and Beijing.
The S&P 500 index gained 13.39 points, or 0.5%, to 2,886.73. The benchmark index rose 4.4% last week, its best weekly performance of 2019. It's now about 2% below its record set on April 30. The Dow Jones Industrial Average rose 78.74 points, or 0.3%, to 26,062.68. The Nasdaq composite climbed 81.07 points, or 1.1%, to 7,823.17. The Russell 2000 index of smaller companies gained 9.17 points, or 0.6%, to 1,523.56.
Jingyi Pan, market strategist at IG in Singapore, warned against getting hopes up too much about a resolution on U.S.-China trade issues. "The seemingly complicated matter of a U.S.-China trade deal appears highly unlikely to be resolved from a high-level meeting between the two presidents," Pan said.
"Given the return of the U.S.-China tariffs threat to the table, look to Asia markets to waffle along." ENERGY: Benchmark U.S. crude rose 64 cents to $53.90 a barrel. It slid 1.4% to $53.26 a barrel on Monday. Brent crude oil, the international standard, was up 52 cents at $62.81 a barrel.
CURRENCIES: The dollar inched up to 108.61 yen from 108.60 yen on Monday. The euro rose to $1.1320 from $1.1307.