The claim, which he has made before on Twitter, has been judged untrue by numerous fact-checkers. The new president’s willingness to bring it up at a White House reception in the State Dining Room is an indication that he continues to dwell on the implications of his popular vote loss even after assuming power.
Mr. Trump appears to remain concerned that the public will view his victory — and his entire presidency — as illegitimate if he does not repeatedly challenge the idea that Americans were deeply divided about sending him to the White House to succeed President Barack Obama.
Mr. Trump received 304 electoral votes to capture the White House, but he fell almost three million votes short of Hillary Clinton in the popular vote. That reality appears to have bothered him since Election Day, prompting him to repeatedly complain that adversaries were trying to undermine him.
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 asserted that between three million and five million unauthorized immigrants voted 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 H. Hoyer, Democrat of Maryland, who attended the meeting, said that Mr. Trump also talked about the size of the crowd for his Inaugural Address.
“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 did not “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 to repeal and replace Mr. Obama’s health care law, pass a large investment in the nation’s infrastructure, make changes to the country’s immigration laws and overhaul 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 while Mr. Trump is in office than they were during Mr. Obama’s tenure. Mr. Obama famously disliked socializing with members of Congress.
Referring to Democrats, Mr. Cornyn 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 issues involving intellectual property rights, 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 city that he spent more time mocking than praising during his campaign.
In his Inaugural Address, the president criticized the political establishment, saying the people assembled behind him — including the leaders he met with on Monday — had “reaped the rewards of government while the people have borne the cost.”
White House officials said the meeting 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 Ms. Pelosi 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.”
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, 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 because of 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, officials said, was another step in that process.