The Dow Jones alone jumped almost 700 points, nearly reversing the five months worth of gains lost yesterday. Hong Kong's Hang Seng advanced 0.8 percent to 30,790.83, while the Shanghai Composite index rose 1.1 percent to 3,166.65.
Treasury Secretary Steven Mnuchin told Fox News that he is "cautiously hopeful" that a trade deal can be reached with China.
U.S. stocks tumbled on both Thursday and Friday last week after President Donald Trump unveiled tariffs on up to $60 billion of Chinese imports and vowed to counter China's alleged "theft" of American intellectual property.
"There are some tentative signs that fears of an escalation of trade tensions are beginning to ease", Craig Erlam, a market analyst at OANDA wrote in a note to clients. The Nasdaq climbed about 3.25 percent as investors were reassured that a damaging trade war might be avoided.
"Equities are extending their rebound as investors breath a collective sigh of relief that a global trade war looks to be off the menu (China and USA negotiating, several exemptions)".
US President Donald Trump announced the tariffs against Chinese goods on Thursday, saying they were a response to allegations of intellectual property theft by China.
Facebook shares traded 2 percent weaker at US$156.19 as of 1.26pm in NY, down from a record high of US$193.09 last month.
Last week, the three main United States indexes posted their steepest weekly declines since January 2016 as the fears of a global trade war added to jitters about a faster pace of USA interest rate hikes and fears of increased regulations to the high-flying technology sector in the wake of Facebook's data scandal.
Japan's Nikkei, meanwhile, erased earlier losses of 1.3 per cent to end 0.7 per cent higher.
"The reality is that there probably isn't a trade war, as evidenced by the fact that there's discussion going on between China and the U.S.to work these things out".
South Korea's benchmark share index rose 0.8 per cent.
Brent crude futures were up 9 cents at $70.54 a barrel. President Trump said last week he wants China to lower its 25 percent tariffs on USA automobiles exported to China. "The trade tensions imperil growth", said Michael McCarthy of CMC Markets in a report.