WASHINGTON — President Trump used his first official meeting with congressional leaders on Monday to gripe about his loss of the popular vote, falsely telling the lawmakers that he would have won a majority if millions of illegal immigrants had not voted against him.

The claim, which he has made before on Twitter, has been judged to be untrue by numerous fact-checkers. But the new president’s willingness to bring it up at Monday’s White House reception in the State Dining Room is an indication that he remains focused on his election even after assuming power.

Mr. Trump won 304 electoral votes to capture the presidency, but he fell almost three million votes short of Hillary Clinton in the popular vote. That reality appears to have bothered the president since Election Day, prompting him to repeatedly complain that adversaries were trying to undermine his legitimacy.

Moving into the White House appears not to have tempered that anxiety. Several people familiar with the closed-door meeting Monday night, who asked to remain anonymous in discussing a private conversation, said Mr. Trump used the opportunity to brag about his victory.

As part of that conversation, Mr. Trump made the assertion about illegal immigrants voting in huge numbers for Mrs. Clinton. That is similar to a Twitter message he posted in late November that said he would have won the popular vote “if you deduct the millions of people who voted illegally.”

Voting officials across the country have said there is virtually no evidence of people voting illegally, and certainly not millions of them. White House officials did not respond to requests for a comment on Mr. Trump’s discussion of the issue.

Representative Steny Hoyer, Democrat of Maryland, who attended the meeting, said on CNN that Mr. Trump also talked about the size of the crowd for his inauguration speech.

“It was a huge crowd, a magnificent crowd. I haven’t seen such a crowd as big as this,” Mr. Hoyer told CNN, quoting Mr. Trump. He added that Mr. Trump didn’t “spend a lot of time on that, but it was clear that it was still on his mind.”

The president’s comments about the election results and his inauguration came as he gathered the bipartisan leadership of Congress for a White House reception. He also sought to build support for an ambitious legislative agenda despite days earlier castigating the very institution he needs to approve it.

Mr. Trump has said he intends to press Congress to move quickly on a repeal and replacement of President Obama’s health care law, a large investment in the nation’s infrastructure, changes to the country’s immigration laws, and an overhaul of the tax system.

Senator John Cornyn, Republican of Texas, called the meeting a “good sort of get-to-know-you session” and noted that “relationships count for a lot in this business.”

Mr. Cornyn said he thought such sessions would be more frequent during Mr. Trump’s time in office than it was during President Barack Obama’s tenure. Mr. Obama famously disliked spending social time with members of Congress.

Referring to Democrats, he said, “They said they’d never been over to the White House for anything like this before.”

Representative Nancy Pelosi of California, the Democratic leader, said it was an “interesting” meeting. Along with health care and infrastructure, she said they discussed China and currency manipulation, as well as intellectual property right issues, which she said were a point of agreement.

“We talked about the Affordable Care Act and said what the Affordable Care Act has been successful in doing is improving quality, expanding access and lowering costs,” she told reporters. “And any proposal that they might have that does that – we’d be interested in hearing about.”

Even with Republicans in control of Congress, Mr. Trump will have to build relationships in a town that he spent more time mocking than praising during his presidential campaign.

In his inaugural address, the president criticized the establishment in Washington, saying the people assembled behind him — including the leadership he would soon meet with on Monday at the White House — had “reaped the rewards of government while the people have borne the cost.”

White House officials said the meeting on Monday between the president and bipartisan leaders from the House and Senate was designed to press the lawmakers on the need to move quickly.

The reception included, among others, House Speaker Paul D. Ryan of Wisconsin and Senator Mitch McConnell of Kentucky, the majority leader, as well as the minority leaders of the House and Senate, Representative Nancy Pelosi of California and Senator Chuck Schumer of New York.

“The American people are frustrated with the lack of progress here in Washington, and the president wants no delay in addressing our most pressing issues,” said Sean Spicer, the White House press secretary. “He’s taking every opportunity to forge strong bonds with congressional leaders on both sides of the aisle.”

To that end, the leadership arrived on Monday for a reception in the State Dining Room that included light appetizers: meatballs, shrimp cocktail and sliders. As the group sat around a dining room table for photographs, Mr. Trump described his interactions with lawmakers.

A “beautiful, beautiful relationship,” Mr. Trump told reporters.

That has not always been the case. Before Mr. Trump secured the Republican nomination last year, Mr. Ryan pointedly declined to endorse him. At one point, Mr. Ryan said he was “not ready” to back Mr. Trump after his remarks about women and Hispanics and his divergence from Republican orthodoxy.

That relationship slowly improved after Mr. Trump became the party’s nominee and later won the election to become the 45th president. Monday’s reception was another step in that process, officials said.