Stocks rallied on Tuesday as Wall Street breathed a sigh of relief after China's president said he would work to "open" the country's economy, easing trade war fears.

The Dow Jones industrial average closed 428.90 points higher at 24,408, with Boeing as the best-performing stock in the index. The S&P 500 gained 1.8 percent to close at 2,656.87, with energy leading nine of 11 sectors higher. The Nasdaq composite advanced 1.7 percent to 7,094.30.

Chinese President Xi Jinping discussed plans Tuesday to further open up the country's economy, with measures including lowering import tariffs on autos, enforcing legal intellectual property of foreign groups and reducing duties on other consumer products.

Crude prices rose more than 3 percent, breaking above USD 65 per barrel. Oil's strong gains boosted energy stocks. The Energy Select Sector SPDR fund (XLE) surged 3.3 percent and posted its best day since Nov. 30, 2016.

Xi's address also appeared to boost market sentiment overseas Tuesday, with markets in Europe and Asia trading higher during their respective sessions. Investors have been on edge recently on fears that the U.S. and China could engage each other in a trade war.

The moves Tuesday follow a roller-coaster session for Wall Street. The Dow rallied more than 400 points in Monday's session before erasing the majority of its gains, as political turbulence within the U.S. administration rattled sentiment.

The FBI raided the New York office and residence of Michael Cohen, the personal attorney to President Donald Trump. According to NBC News, which cited sources, agents were looking for evidence that was related to a USD 130,000 payment the lawyer made to porn star Stormy Daniels, prior to the 2016 election.

Stocks have been considerably more volatile this year than in 2017. Through Monday's close, the S&P 500 has posted 27 moves greater than 1 percent. Last year, the index posted just eight.

Elsewhere, shares of Facebook rose more than 4 percent as CEO Mark Zuckerberg testified in front of Congress following news that Cambridge Analytica was able to access the private data of millions of users without their consent.