Democrats raised more questions on Friday about President Biden’s viability as a candidate, as rank-and-file lawmakers continued to call on him to end his re-election bid and the president resisted their entreaties, privately defending his decision to continue running.

One day after a serviceable news conference that had been meant to quell the growing resistance within the party to Mr. Biden’s candidacy, lawmakers returned to their home districts anxious and uncertain about how to proceed. And their leader made it clear that his members still harbored deep concerns over the president’s candidacy.

Representative Hakeem Jeffries, Democrat of New York and the minority leader, met one-on-one at the White House with Mr. Biden on Thursday night to discuss the deep concerns many of his members harbor about his ability to defeat former President Donald J. Trump in November.

In a letter to colleagues on Friday that notably did not endorse Mr. Biden’s decision to stay in the race, Mr. Jeffries did not reveal what he had said to the president, but said he had passed along what he had been hearing from Democrats — many of whom have told him over the past week that the president must step aside.

“In my conversation with President Biden, I directly expressed the full breadth of insight, heartfelt perspectives and conclusions about the path forward that the caucus has shared in our recent time together,” Mr. Jeffries wrote.

On Friday, during an at-times tense virtual meeting with members of the Congressional Hispanic Caucus, Mr. Biden pushed back on Representative Mike Levin, a vulnerable California Democrat, who spoke up to say he thought the president needed to step aside.