Stocks surged on Tuesday after President Donald Trump said he will be meeting with his Chinese counterpart, Xi Jinping, at the upcoming G-20 summit, boosting hope for a U.S.-China trade deal.

The Dow Jones Industrial Average jumped 363 points as Apple and Boeing outperformed. The S&P 500 climbed 1.2% while the Nasdaq Composite advanced 1.8%. The S&P 500 also traded about 1% from its all-time intraday high of 2,954.13, which was reached May 1.

Trump said in a tweet he "had a very good telephone conversation " with Xi. He added: "We will be having an extended meeting next week at the G-20 in Japan. Our respective teams will begin talks prior to our meeting." The summit will start on June 28.

"Certainly, there's ground for optimism," said Michael Geraghty, equity strategist at Cornerstone Capital Group. "However, we have to remember there have been a lot of negotiations between China and the U.S. where they seem to be close to a deal and then things fell apart."

Hope for a U.S.-China trade deal diminished last month after both countries raised tariffs on billions of dollars worth of their goods. Trump also floated the possibility of imposing tariffs on more Chinese imports.

Boeing and Caterpillar shares, two trade bellwethers, rose 2.3% and 2.9%, respectively. Deere shares also gained more than 3%. Semiconductor stocks jumped on Trump's tweet. The VanEck Vector Semiconductor ETF (SMH) surged more than 4%, led by 6% gains from Nvidia and Micron Technology.

Stocks also got a boost as investors bet the Federal Reserve will set the stage for more accommodative monetary policy at this week's meeting.

The Fed is expected to leave rates unchanged at this meeting, which starts Tuesday. However, investors will monitor whether policymakers at the central bank lay the groundwork for rate cuts later in the year. Traders are pricing in three rate cuts before year-end, according to the CME Group's FedWatch tool.

Hope for looser monetary policy eased pressure in equities this month. The major indexes entered Tuesday's session up at least 5% this month.

The Fed's decision is scheduled to be announced Wednesday at 2 p.m. ET. Fed Chair Jerome Powell will also hold a news conference after the announcement.

"Short of easing tomorrow (about 20% priced in), Powell needs to send a strong enough message to the market" that rate cuts are coming, Gregory Faranello, head of U.S. rates at Amerivet Securities, said in a note. "I do feel, though, the Fed needs to take back some control here. We have gone from the market chasing the Fed (4 hikes) to the Fed chasing the market (3 cuts) in a very short period of time."

The meeting comes after jobs growth and manufacturing activity in May slowed down. This, coupled with lingering worries over U.S.-China trade has led to increasing worries over the global economy.

Investors also cheered the prospects of more stimulative measures from Europe. Mario Draghi, president of the European Central Bank, said Tuesday: "In the absence of improvement, such that the sustained return of inflation to our aim is threatened, additional stimulus will be required."

Draghi's comments sent the euro sliding against the dollar. They also jolted European stocks. The Stoxx 600 index climbed more than 1%, along with the German Dax and the French CAC 40.

Trump criticized Draghi's remarks, noting additional ECB stimulus makes it "unfairly easier " for Europe to compete with the U.S.

—CNBC's Sam Meredith contributed to this report.