WASHINGTON — During a private meeting with congressional leaders on Monday, President Trump asserted that between three million and five million unauthorized immigrants had voted for his Democratic opponent and robbed him of a victory in the national popular vote.

There is no evidence to support the claim, which has been discredited repeatedly by numerous fact-checkers.

That did not stop Sean Spicer, the White House press secretary, from standing by the president’s words on Tuesday during a briefing with reporters at the White House. “As I said, I think the president has believed that for a while based on studies and information he has,” Mr. Spicer said.