Japan's benchmark Nikkei 225 added 1.7% to 21,321.17 in early trading. Australia's S&P/ASX 200 rose 1.0% to 6,637.70. South Korea's Kospi was also up 1.0% at 2,119.80. Hong Kong's Hang Seng gained 2.4% to 28,158.85, while the Shanghai Composite added 1.2% to 2,925.68.
Markets also got a boost after the head of the European Central Bank said it was ready to cut interest rates and provide additional economic stimulus if necessary.
The remarks put the spotlight on the U.S. Federal Reserve, which has its own decision on interest rates scheduled later in the day. Many think the U.S. central bank may be headed for its first interest rate cut in over a decade sometime later this year.
On Wall Street, the S&P 500 index climbed 28.08 points, or 1% to 2,917.75. The Dow gained 353.01 points, or 1.4%, to 26,465.54. The Nasdaq jumped 108.86 points, or 1.4%, to 7,953.88.
The Russell 2000 index of smaller companies added 17.48 points, or 1.1%, to 1,550.23.
It was the second straight gain for the market, extending a strong rebound for stocks in June after a steep sell-off last month.
The benchmark S&P 500 is now less than 1% below its all-time high set on April 30. The Dow is 1.4% below its record high set October 3. The Nasdaq is about 2.5% below its record close set on May 3.
Analysts acknowledged an immediate resolution to the trade conflict isn't expected, but the confirmation that Trump and Xi plan to talk at the G-20 in Osaka was cause for some optimism while warning that risks remain.
"While this certainly is a near-term boost for markets, the question as to what can be resolved by the two leader's meeting that had not been done so despite months of discussions keeps this as a risk factor," said Jingyi Pan, market strategist at IG in Singapore.
Two weeks ago, Fed Chair Jerome Powell set off a rally on Wall Street 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 crimp growth. Any continued escalations could put the brakes on what is poised to be the longest economic expansion in U.S. history.
Investors collectively envision a Fed rate cut by July and possibly further cuts after that. Some even expect a rate cut this week. Many economists, though, think the Fed will wait until September at the earliest to announce its first drop in its benchmark short-term interest rate since 2008 and might not cut again in 2019. A few Fed watchers foresee no rate cut at all this year.
Benchmark crude oil rose 6 cents to $53.96 a barrel. It rose 3.8% to $53.90 a barrel Tuesday. Brent crude oil, the international standard, fell 4 cents to $62.10 a barrel.
The dollar rose to 108.48 yen from 108.27 yen on Tuesday. The euro weakened to $1.1193 from $1.1191.
AP Business Writers Damian J. Troise and Alex Veiga contributed to this report.