The Wall Street Journal also reported that U.S. and Chinese officials are working to improve U.S. access to China's markets.

The Financial Times reported China has offered to buy more semiconductors from the U.S. to help cut its trade surplus with the U.S. Shares of Qualcomm and Intel rose 4.6 percent and 6.3 percent, respectively, on the news.

Financials rose sharply, with the Financial Select Sector SPDR S&P Fund (XLF) up 3.3 percent. The XLF posted its biggest one-day gain since November 2016.

The Dow Jones industrial average surged 669.40 points to 24,202.60, with Microsoft as the best-performing stock in the index. The Dow also had its biggest one-day percentage gain since August 2015. The gained 2.7 percent to close at 2,658.55 — bounce off its 200-day moving average — with technology and financials leading all sectors higher. The Nasdaq composite advanced 3.3 percent to 7,220.54 with Apple and Amazon both rising.

Stocks closed sharply higher on Monday, bouncing back from strong losses in the previous session as trade tensions between the U.S. and China appeared to ease.

Investors "have apparently recognized that a trade war is in no one's best interests and therefore extremely unlikely," said Jeremy Klein, chief market strategist at FBN Securities, in a note. "Specifically, the President merely wants to fulfill a campaign promise while China will only enact token countermeasures to appease its citizens."

Markets overseas also jumped on Monday. In Asia, some indexes rose after news surfaced that the U.S. had agreed to excuse South Korea from steel levies. Meantime in Europe, stocks were lower as investors failed to shake off trade war worries.

Wall Street finished Friday's session deep in the red on Friday, with the Dow dropping more than 400 points by the close — closing at its lowest level since November and finishing in correction territory, as it was 11.6 percent down from its 52-week high. The S&P 500 ended Friday's session just outside of correction territory.

Last week, President Donald Trump signed an executive memorandum that would inflict tariffs on Chinese imports — of up to $60 billion. China retaliated with their own set of levies, drawing up a list of 128 U.S. products that could be possible retaliation targets.

"The S&P 500 is having difficulty keeping its head above water this year," said Jack Ablin, founding partner of Cresset Wealth. "While fundamentals are conducive for growth, policy uncertainties related to trade are keeping investors off balance."

Social media firms continue to be under fire, as abuse of people's data remains a key topic of discussion. Last week, reports emerged alleging that Cambridge Analytica, an analytics company, had gathered data from 50 million Facebook profiles without the permission of its users. The stock tanked more than 10 percent last week, pressuring the broader tech sector.

While Facebook have since come out to apologize and try to rectify the matter, concerns remain.

Facebook shares for most of the session after the Federal Trade Commission announced it was investigating the company's data practices. Shares of Google-parent Alphabet also declined on the news, before rebounding to close 2.7 percent higher.

In other corporate news, Boeing shares rose 2.5 percent after the company announced it delivered its first 787-10 Dreamliner jet to Singapore Airlines over the weekend. Boeing had been under pressure lately because it was seen as vulnerable to a trade war.

Meanwhile, Dollar Tree rose 3.6 percent after Piper Jaffray upgraded the stock to "overweight" from "neutral," citing, among other factors, good investments at its Family Dollar unit.

Microsoft led the way for tech stocks, rising 7.6 percent after Morgan Stanley said the company could reach $1 trillion in market cap because of its cloud adoption.