Even as U.S. President Donald Trump starts reaching out to lawmakers and business and union leaders to sell his policies, he's still making false claims about election fraud.

During a bipartisan reception with lawmakers at the White House Monday evening, Trump claimed the reason he'd lost the popular vote to his Democratic rival was that three million to five million immigrants living in the U.S. illegally had voted. That's according to a Democratic aide familiar with the exchange who spoke on condition of anonymity to discuss the private meeting.

There is no evidence to support Trump's claim.

The assertion appeared to be part of a developing pattern for Trump and his new administration in which falsehoods overshadow outreach efforts.

White House press secretary Sean Spicer reiterates it's unsubstantiated voter fraud allegations 0:39

After a contentious weekend, Trump began his first full week as president bounding from one room of the White House to another as he played host to business, labour and congressional leaders. Again and again, he ordered aides to summon journalists from their West Wing workspace at a moment's notice for unscheduled statements and photo opportunities.

Among those meetings: a reception at the White House for congressional leaders of both parties, with plenty of meatballs and small talk.

But what was supposed to be a lighthearted get-together was overshadowed by Trump's debunked assertion about the popular vote.

In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally —@realDonaldTrump

Trump's comments were similar to claims he made on Twitter in late November that he had won the Electoral College in a "landslide" and "won the popular vote if you deduct the millions of people who voted illegally." Hillary Clinton won the popular vote by nearly 2.9 million votes, despite losing the electoral college. There is no evidence that voter fraud significantly affected the vote.

Republicans split on Trump's claim

The top three Senate Republicans refused on Tuesday to disavow Trump's false claim that millions of illegally cast ballots cost him the popular vote.

The comments from Senate majority leader Mitch McConnell and his top lieutenants suggested that some leading Republicans would rather follow Trump into the realm of "alternative facts" than confront the new chief executive.

"It does occur," McConnell told reporters at the Capitol Tuesday on the issue of election fraud. "There are always arguments on both sides about how much, how frequent and all the rest.… The notion that election fraud is a fiction is not true."

Senate majority leader Mitch McConnell is joined by, from left, senators Cory Gardner, John Barrasso, John Thune and Senate majority whip John Cornyn on Capitol Hill in Washington on Tuesday. (J. Scott Applewhite/Associated Press)

The No. 2 Senate Republican, John Cornyn of Texas, also passed up a chance to dispute Trump's claim Tuesday, saying, "I'm not going to re-litigate that. It's time to move on."

And the No. 3 Senate Republican, John Thune of South Dakota, said he didn't know whether three million to five million votes were cast fraudulently, which would be larger than the population of all but the biggest U.S. cities.

"There's always a certain amount of irregularity that goes on in elections, some places perhaps more so than others. How you quantify that I'm not sure, but he must have his methodology," Thune said.

Not all Republicans were unwilling to dispute Trump.

Lindsey Graham, the South Carolina Republican senator, while referring to the president's voter fraud claims said, "This needs to stop."

Republican Lindsey Graham urges new president to 'share or recant' 0:57

Graham implored Trump to either release evidence that backed his claims or recant them altogether.

House Speaker Paul Ryan told reporters on the illegal voting claim: "I've seen no evidence to that effect and I've made that very, very clear," though he declined to get drawn into further comment.

Arizona Republican Senator John McCain said, "Do I believe it? I have no evidence of it." But McCain, who did not support Trump for president, demurred when asked whether Trump should stop uttering falsehoods.

"I did not support the president of the United States in the election, so I don't really have any place where I tell him what he should do," he said.