U.S. stocks looked headed for a strong bounce on Tuesday, as traders cheered promises by Chinese President Xi Jinping to open the country’s markets.

Xi’s remarks, made at a major conference in Asia, may help to soothe fears of an all-out trade war between Beijing and Washington, a factor that has weighed on equities. The market’s updraft came after late-session jitters linked to reports that the Federal Bureau of Investigation raided the office of President Donald Trump’s personal lawyer helped to erase much of Monday’s rally.

What did the main benchmarks do?

Dow Jones Industrial Average futures YMM8, +1.29% surged 304 points, or 1.3%, to 24,311, while S&P 500 futures ESM8, +1.15% gained 31.15 points, or 1.2%, to 2,650.25. Nasdaq-100 futures NQM8, +1.44% jumped 98.25 points, or 1.5%, to 6,595.50.

Stock markets sold off toward the end of Monday’s session on news of the FBI raid. The Dow industrials DJIA, +0.19% which had surged by as much as 440 points during the session, closed up 46.34 points, or 0.2%, at 23,979.10.

The S&P 500 SPX, +0.33% fell back from a gain of 1.9% to close just 0.3% higher, a move that made for the worst final hour of trading for the index since Sept. 27, 2011. The Nasdaq Composite Index COMP, +0.51% gained 2.3% at one point, but finished up only 0.5%.

Need to know: ‘Curbing our enthusiasm’—big bank takes a knife to its S&P 500 target

What’s driving markets

A global equity rally was triggered as Chinese President Xi told the Boao Forum that Beijing plans to give foreign companies greater access to financial and manufacturing sectors. He also talked about a cut in tariffs on car imports and an improvement in protection of intellectual property, among other measures. While many of the measures had been previously touted by Xi, investors cheered the lack of any escalation in rhetoric.

“In a world aspiring for peace and development, the Cold War and zero-sum mentality look even more out of place,” said Xi.

Trump has threatened tariffs on up to $150 billion of Chinese products, which Beijing has answered with proposed levies of its own.

Trade optimism could, for now, help the market shake off the FBI’s seizure of records held by Michael Cohen, a personal lawyer for Trump. The records are related to a $130,00 payment to adult-film actress Stormy Daniels, who alleges she had a brief affair with the president. Trump dismissed the raid as a “witch hunt.”

Read: Here’s what FBI raid on Trump lawyer’s office means for the stock market

Elsewhere, the U.S. is preparing for a possible military strike against Syrian President Bashar al-Assad over a suspected chemical-weapons attack that killed civilians. “It will be met, and it will be met forcefully—when, I will not say,” Trump said Monday evening, ahead of a meeting with senior military leaders.

What are strategists saying?

“While China may still be teeing up its reciprocal response to the $100 [billion] in Tariffs from the U.S., Xi has shown good intentions via his speech. We are still clinging on with gritted teeth to our belief that a trade war will be averted,” said Jasper Lawler, head of research at LGC, in a note to clients.

An upbeat response from Trump might give stocks additional incentive to move higher, said Chris Beauchamp, chief market analyst at IG, in a note to clients. Still, he urged investors stay a little cautious. “Now is not the time to chase equities, particularly with earnings season just days away, but those who bought into last week’s lows will be keeping their fingers crossed that this bounce has a bit more life in it yet,” he said.

Opinion: These two trading patterns could trigger the long-awaited stock market ‘melt-up’

What data are in focus?

Ahead of the open, the National Federation of Independent Businesses index of small-business optimism fell to 104.7 in March.

A reading on producer prices for the same month is due at 8:30 a.m. Eastern, followed by a report on February wholesale inventories at 10 a.m.

Read: The economy is fine now, but watch out for 2020, top economist says

Federal Reserve Bank of Dallas President Robert Kaplan said he expects the Fed to increase rates twice more this year, but added that the pace of rate increases could ease in the years ahead due to slowing growth. He made the comments in a Bloomberg TV interview in Beijing late Monday.

Which stocks could be active?

Shares of VeriFone Systems Inc. PAY, -1.12% surged 52% in premarket after the payment and business services provider said it has agreed to a $3.4 billion private-equity acquisition by a group led by Francisco Partners. The deal is worth $23.04 a share in cash, a premium of 54% on Verifone’s closing price Monday of $15.

Tenneco Inc. TEN, -0.05% said it planned on buying Federal-Mogul, a manufacturer of parts for cars and the aerospace industry, from Icahn Enterprises L.P. IEP, -0.60% in a deal valued at $5.4 billion. Shares of Tenneco rose 2.8% in premarket trade, while those for Icahn Enterprises were halted.

Energous Corp. WATT, +5.25% rallied 27% in premarket after the developer of wire-free charging technology said the Federal Communications Commission has approved its near-field transmitter WattUp.

Tupperware Brands Corp. TUP, -0.38% fell nearly 5% after the plastic-container maker lowered its first-quarter earnings guidance.

Facebook Inc. FB, +0.46% shares rose around 1% in premarket. Mark Zuckerberg, chief executive officer of the social-media website, is due to testify in a joint hearing held by two Senate committees on Tuesday around 2:15 p.m. Eastern. Zuckerberg is expected to discuss his company’ handling of a privacy controversy involving Cambridge Analytica.

Read: Here are the changes Facebook has announced ahead of Zuckerberg testimony

First-quarter earnings season will kick off in earnest on Thursday and Friday, as BlackRock Inc. BLK, +0.23% Wells Fargo & Co. WFC, +0.04% and JPMorgan Chase & Co. JPM, +1.20% are all expected to report results.

What are other markets doing?

Asian stocks got a lift after the Chinese president’s speech, with Hong Kong’s Hang Seng Index HSI, +1.65% HSI, +1.65% rising 1.5%. European stocks SXXP, +0.51% hit multiweek highs as a global equity rally took hold.

Gold futures GCM8, +0.05% were steady at $1,341.50 an ounce. The ICE U.S. Dollar Index DXY, -0.15% flattened out at 89.794. Oil prices CLK8, +1.66% surged 2.1% to $64.77 a barrel, climbing as trade-war tensions lifted.