Sentiment also got a boost from reports that the White House plans to delay new tariffs on car and auto parts imports from Europe by up to six months.
Mnuchin also said he expected to travel soon to Beijing to resume talks on the trade dispute that has rattled financial markets and cast doubt over the global economic outlook.
But the rally fizzled in Asia, where Japan's benchmark Nikkei 225 slipped 0.7% to 21,050.23. South Korea's Kospi lost 0.7% at 2,078.49. Australia's S&P/ASX 200 fell 0.1% to 6,290.10. Hong Kong's Hang Seng was little changed, inching up less than 0.1% to 28,284.00, while the Shanghai Composite rose nearly 0.1% to 2,941.90.
On Wall Street, the S&P 500 index gained 0.6% to 2,850.96. The Dow Jones Industrial Average rose 0.5% to 25,648.02.
The Nasdaq, which is heavily weighted with technology stocks, added 1.1% to 7,822.15.
Small-company stocks lagged the market. The Russell 2000 index picked up 0.3% to 1,548.27.
Stocks have been whipsawed this week by worries over the worsening relationship between China and the U.S. and its impact on the broader global economy.
Tensions between the world's two biggest economies intensified over the last week. The Trump administration more than doubled tariffs on $200 billion in Chinese imports and spelled out plans to target the $300 billion worth that aren't already facing 25% taxes. The escalation covers everything from sneakers to toasters to billiard balls. The Chinese have retaliated by hiking tariffs on $60 billion in U.S. imports.
"The only real piece of good news is that the U.S. has announced it will defer its decision on auto tariffs to November, perhaps aimed at placating allies such as Germany and Japan as it fights a trade war with China," said Chang Wei Liang, of the Asia & Oceania Treasury Department at Mizuho Bank in Singapore.
The U.S. and Japan also are holding trade talks, and trade issues are expected to be on the agenda at the summit of the Group of 20 industrial nations later this month in Japan.
ENERGY: Benchmark U.S. crude gained 35 cents to $62.37 a barrel in electronic trading on the New York Mercantile Exchange. It rose 0.4% to $62.02 per barrel Wednesday. Brent crude, the international standard, added 35 cents to $72.12 per barrel.
CURRENCIES: The dollar fell to 109.47 Japanese yen from 109.59 yen. The euro inched up to $1.1211 from $1.1206.
Follow Yuri Kageyama on Twitter https://twitter.com/yurikageyama
On Instagram https://www.instagram.com/yurikageyama/?hl=en