Tensions soared Wednesday over President Trump’s decision to pull U.S. troops from Syria, with the House voting overwhelmingly to rebuke him and a subsequent confrontation at the White House that led to Democratic leaders walking out on the president.

House Speaker Nancy Pelosi, California Democrat, said that when she delivered news of the rebuke, Mr. Trump had a “meltdown” and called her a “third-rate politician.”

Republicans said it was Mrs. Pelosi whose conduct was outrageous. They said her walkout was unbecoming and her push toward impeaching Mr. Trump is poisoning government at the highest levels.

The White House canceled a classified briefing for Congress scheduled for later this week that was intended to give lawmakers inside information on Syria. That fueled Democrats’ complaints that Mr. Trump is trying to shut them out of a role in his decision-making.

Mr. Trump signaled that he won’t be bullied into changing, saying Syria is “not our problem” — though he did try to cajole Turkey to pull back from its invasion of a Kurdish region in Syria, a move that has led to chaos on the ground.

The House voted 354-60 to condemn the president’s surprise decision last week to withdraw U.S. forces. All Democrats and a majority of Republicans voted in favor of the rebuke, saying the president has squandered years of goodwill and U.S. credibility.

“How can America be trusted to keep its word when we make impulsive decisions that have an immediate and catastrophic impact on millions of people?” said Rep. Eliot L. Engel, New York Democrat and chairman of the House Foreign Affairs Committee.

Yet the rebuke is just words, and Republican leaders said that other than slapping more sanctions on Turkey, there is not a lot Congress can do to insert itself into the situation. Forcing Mr. Trump to reverse himself is unlikely.

“I mean, what tools do we have?” Senate Majority Leader Mitch McConnell, Kentucky Republican, asked reporters who peppered him with questions. “Any president has a lot of latitude in deploying troops.”

Mr. McConnell repeatedly called Mr. Trump’s decision “a mistake,” marking some of the most serious criticisms he has aimed at Mr. Trump over the course of his presidency.

But he seemed pessimistic that more congressional chiding along the lines of the House’s anti-Trump broadside would change the president’s decision.

“It shouldn’t have been done, and [I’m] hoping that he would reverse course. There seems to be no evidence of it so far, but I think it was a mistake,” Mr. McConnell said.

U.S. lawmakers say Mr. Trump’s decision is a betrayal of the Kurds, who now find themselves battling Turkey in a fight that pits two U.S. allies against each other. Mr. Trump’s critics say the U.S. troops served as a buffer between the Kurds and Turkey and deterred Iranian and Russian mischief.

Now those constraints are gone and the region has descended to violent chaos — including the danger that Islamic State fighters will escape confinement and return to terrorism.

“Leaving Northwest Syria does not resolve the problem that brought us there in the first place. It only creates more,” said Rep. Michael T. McCaul, a Texas Republican who helped write the resolution rebuking Mr. Trump.

Voting for the resolution were 225 House Democrats and 129 Republicans — more than double the 60 Republicans who voted “no.” House Republicans’ top leaders voted for the rebuke.

Democratic congressional leaders said they hoped that high tally would persuade Mr. Trump to do an about-face. Instead, they walked out of an afternoon meeting when the president lashed out.

“This was not a dialogue,” said Senate Minority Leader Charles E. Schumer, New York Democrat, calling it a “diatribe.”

Republicans who emerged from the White House said Democrats were the ones who behaved poorly.

If Mrs. Pelosi had stayed instead of storming out, then she would have been part of a productive meeting in which generals outlined plans to keep a small residual force in Syria to protect U.S. interests, said House Minority Leader Kevin McCarthy, California Republican.

Mr. Trump renewed his feud with sometime ally Sen. Lindsey Graham, a South Carolina Republican who has called the president’s decision “the biggest mistake of his presidency.”

He said Mr. Graham, a frequent golfing buddy, should stop giving him advice and stick to approving his judges and investigating whether President Barack Obama tried to spoil his chances during the 2016 campaign.

Mr. Graham, who is working on a bill to slap sanctions on Turkey, said he “won’t be quiet” about national security.

Rep. Liz Cheney of Wyoming, chair of the House Republican Conference, announced similar legislation in the lower chamber.

Her bill personally targets Turkish President Recep Tayyip Erdogan and demands that the administration figure out his net worth and report the figure to Congress. Her bill would also block key Turkish officials from entering the U.S. and deny American military assistance to the country.

Despite his defiance, Mr. Trump has made some concessions, including agreeing to leave a small force in Syria.

He also is working on persuading Mr. Erdogan to curtail his attack on the Kurds. He is deploying Vice President Mike Pence and Secretary of State Mike Pompeo to talk with the Turkish leader on Thursday.

A letter Mr. Trump wrote last week to Mr. Erdogan also surfaced Wednesday and showed the U.S. leader badgering his counterpart.

“History will look upon you favorably if you get this done the right and humane way,” Mr. Trump said. “It will look upon you forever as the devil if good things don’t happen. Don’t be a tough guy. Don’t be a fool!”

⦁ Stephen Dinan contributed to this report.

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