The Dow Jones industrial average rose 100 points, or 0.38%, to 26,700, while the Standard & Poor's 500 index increased 18 points, or 0.62%, to 2,960.
In Europe, Frankfurt's trade-sensitive DAX .GDAXI rallied 1%, the most among the major European indexes, while the tech index .SX8P rose 1.9% as chipmakers were boosted by the Huawei relief.
At a meeting on the sidelines of the G20 summit, President Donald Trump offered concessions to his Chinese counterpart Xi Jinping including no new tariffs and reducing restrictions on tech company Huawei.
The JGB market showed little reaction to the Bank of Japan's "tankan" survey of business confidence released on Monday, which showed large manufacturers' business confidence deteriorating to a near three-year low in the April-June quarter.
"I think the Fed expectations in the market are very aggressive".
The blue-chip Swiss index .SSMI gained 0.7% despite stocks being blocked from trading on European Union exchanges after talks to resolve a dispute between Brussels and Switzerland collapsed.
FILE PHOTO: Traders work on the floor at the New York Stock Exchange (NYSE) in New York, U.S., June 17, 2019.
-China trade talks sparked concerns of a global economic slowdown.
But hopes that the Federal Reserve would cut interest rates to preserve a strong run of USA economic growth helped the S&P 500 and the Dow Jones index post their best June performance in generations. "This comes at a time when global PMI data shows continued manufacturing weakness in China, Europe and even the United States".
The Dow opened 0.9%, or 262 points, higher.
Elsewhere in commodities trading, Brent oil for delivery in September rose 2.95% or 1.91 to hit $66.65 a barrel, while the August Gold Futures contract fell 1.76% or 24.85 to trade at $1388.85 a troy ounce.
Wynn Resorts Ltd (WYNN.O) jumped 7.2%, the most on the S&P, as gambling revenue in the Chinese territory of Macau rose more than expected in June.
Coty Inc (COTY.N) tumbled 13.5%, falling the most on the S&P, after the company said it would overhaul its operations and write down about $3 billion in value of its brands acquired from Procter & Gamble Co (PG.N). That puts the index on track for a record high.