(CNN Money) -- Chinese President Xi Jinping gave Wall Street a lift.

The Dow rallied 429 points on Tuesday after Xi said in a speech that the Chinese government plans to "significantly lower" tariffs on imported cars as part of efforts to further open China's economy.

The Nasdaq climbed more than 2%, and the The S&P 500 gained 1.7%. Automakers helped lead the charge: GM, Ford, Honda and Tesla all gained ground.

Xi's conciliatory speech cooled trade tensions between the United States and China. Investors hope Xi's plan will convince the Trump administration to move away from protectionism.

President Trump praised Xi on Twitter on Tuesday. "We will make great progress together!" he said.

"This could provide Trump with an opportunity to back down from his tariff threats while claiming a victory of sorts," Capital Economics' Julian Evans-Pritchard wrote in a research note Tuesday.

The United States-China spat has roiled markets in recent weeks.

Investors fear a full-scale trade war could break out between the world's two largest economies and slow global economic growth.

Trump has proposed tariffs on up to $150 billion of Chinese goods. In retaliation, China said it planned to put $50 billion in tariffs on US planes, cars and soybeans.

Trump complained as recently as Monday about China's 25% tariff on foreign cars.

"Does that sound like free or fair trade," Trump tweeted. "No, it sounds like STUPID TRADE - going on for years!"

Xi didn't mention Trump or the United States in his speech, but he stressed the need for dialogue and warned against a "Cold War mentality."

Although Xi said lowering tariffs on imported cars was part of "a new phase of opening up" China, the Chinese government has mentioned the plan before.

When Trump visited China in November, Chinese officials pledged to "gradually and properly" reduce tariffs on imported vehicles. They didn't give a specific time frame.

"There was little in Xi's speech that we haven't heard before," Evans-Pritchard said. "What he has done, however, is cleverly combined existing reform pledges into a single package."

Investors will now wait to see how the administration responds.

With midterm elections approaching in the fall and Trump's Midwest farm base caught in the US-China fight, "Trump will gladly take any bone that the Chinese throw his way," said Ed Yardeni, president of Yardeni Research. Trump admitted Monday that Chinese tariffs may hurt farmers, but said "we'll make it up to them."

Legal developments also loomed over the market for the second straight day.

The Dow lost most of its gains at the end of the day Monday as news broke that the FBI had raided the office and home of Michael Cohen, Trump's personal lawyer and confidant.

Stocks recovered Tuesday.

"Everybody slept on it and recognized that wherever this leads it's not likely to have a significant economic impact," Yardeni said.

—CNN's Jethro Mullen contributed to this story.

The-CNN-Wire™ & © 2018 Cable News Network, Inc., a Time Warner Company. All rights reserved.