WASHINGTON — The top three Senate Republicans refused on Tuesday to disavow President 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.

McConnell and other top Republicans faced questions after Trump told a group of congressional leaders at the White House Monday night that he would have won the popular vote but for 3 million to 5 million ballots cast by immigrants in the country illegally. Hillary Clinton won the popular vote by nearly 2.9 million votes and there is no indication that significant numbers of voters cast illegal ballots for either candidate.


‘‘It does occur,’’ McConnell told reporters 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.’’

The Kentucky Republican made his comments at the same time Trump’s spokesman, in a briefing at the White House, stuck firmly to Trump’s claim about illegal voting in the November election, though without providing any evidence to back it up. ‘‘He believes what he believes, based on the information he was provided,’’ said press secretary Sean Spicer, without detailing that information.

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 3 million to 5 million votes were cast fraudulently, which would be larger than the population of all but the biggest US 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.

Other Republicans were willing to dispute Trump.

House Speaker Paul Ryan of Wisconsin 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.

Senator John McCain of Arizona said of Trump’s claims, ‘‘Do I believe it? I have no evidence of it.’’ But McCain 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,’’ McCain said.

The varied reactions illustrated a dilemma for GOP lawmakers facing a new president with a strained relationship with the truth. Many Republicans seem to see little upside in contradicting Trump, who remains popular with many GOP base voters.