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.

Boeing and Caterpillar both rose more than 3 percent as concerns of a trade war were alleviated.

The Dow Jones industrial average closed 428.90 points higher at 24,408, with Boeing as the best-performing stock in the index. The 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.

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.

Traders work on the floor of the New York Stock Exchange.

"If you look at President Xi's speech, it was conciliatory and that feels like a de-escalation," said Art Hogan, chief market strategist at B. Riley FBR. "That's what the market wants."

"The problem is reform in China happens slowly," Hogan said.

Shares of U.S. automakers jumped on the news. Ford Motor rose 1.8 percent, while General Motors and Tesla gained 3.3 percent and 5.2 percent, respectively. Fiat Chrysler also climbed 2 percent.

Crude prices rose more than 3 percent, breaking above $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 $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.

"This is a more normal environment. It doesn't feel normal because we're not used to it," said David Spika, president of GuideStone Capital Management.

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.

Zuckerberg said the company did not notify the Federal Trade Commission about the leak, noting: "We considered it a closed case."

—CNBC's Everett Rosenfeld and Huileng Tan contributed to this report.