WASHINGTON—President Biden told congressional Democrats in a letter Monday that he was committed to “running this race to the end” and that it was time for conversations about changing nominees to stop, as public and private calls for him to exit from the contest grow louder.

In the letter, Biden said he had had “extensive conversations” with party leadership, members and voters over the past 10 days and said he wasn’t blind to the concerns about his age and his candidacy that have emerged since his disastrous debate performance. But he said he was heartened by “rock-solid, steadfast support” from many and wouldn’t continue if he wasn’t confident he could beat former President Donald Trump.

A defiant Biden also argued that he had been made the nominee in the Democratic primary process and that to step aside would disenfranchise those voters, though no prominent Democrats chose to challenge him in the primaries. “How can we stand for Democracy in our nation, if we ignore it in our own party,” he wrote. “I cannot do that. I will not do that.”

The president also called in to MSNBC’s “Morning Joe” on Monday, saying he has been talking to voters around the country. “I wanted to make sure I was right, that the average voter out there wanted Joe Biden and I’m confident that they do,” he said over the phone. “I am not going anywhere.”

Biden told the hosts that he had a “neurological physical” in February and continued to argue that he had a bad night during the debate. Asked about the editorial boards and elected officials who have said he should step aside, he said: “I don’t care about what those big names think.”

“I’m getting frustrated by the elites…in the party,” he said. “If any of these guys don’t think I should run, run against me. Announce for president, challenge me at the convention,” referring to the party’s gathering next month.

Also on Monday, the president joined a midday call with top fundraisers, alongside Maryland Gov. Wes Moore and campaign chair Jen O’Malley Dillon. On the call, Biden noted that he is the party’s nominee and said the party needs to focus on Trump, according to one person on the call. Another person on the call said he spoke about the letter to Congress and described his campaigning in Pennsylvania on Sunday. And another donor said Biden conveyed he was in the fight and emphasized Trump’s policy plans.

A sign stating “Restricted Area” is posted in front of the White House in Washington, U.S., July 8, 2024. REUTERS/Kevin Mohatt

Biden also took questions on how he would handle a second debate, what his 30-second pitch is and his position on LGBTQ rights, some attendees said. On a second debate with Trump, Biden said he would respond to “lie after lie after lie,” one donor said.

Biden’s latest attempt to shore up his candidacy came as lawmakers return to Capitol Hill and Democrats are expected to continue conversations about whether to support his candidacy. In a private meeting of senior House Democrats Sunday, several attendees said that they believed Biden should step aside, bringing the number of House Democrats publicly or privately saying he should step aside to about 10.

Others weighed in with cautious remarks Monday. Sen. Jon Tester (D., Mont.), who is locked in a tough re-election fight, told a Billings news outlet that Biden “has got to prove to the American people—including me—that he’s up to the job for another four years.” Rep. Greg Landsman (D., Ohio), also in a competitive race, said Biden needs to be able to make the case that Trump is unfit to be president. “Now’s the time for action, but time is running out,” he said.

While Biden pointed to the will of the party in his letter, polls show significant discontent among Democrats with Biden as their nominee. Some 76% say he is too old to run this year, or about the same share as Republicans who hold that view, according to the latest Wall Street Journal poll. Two-thirds of Democrats would replace Biden on the ballot with another nominee.

The president spent Sunday campaigning in the battleground state of Pennsylvania, as he is bleeding support among Democrats and donors. While Vice President Kamala Harris has the clearest path to step up if Biden withdraws, dissenting Democrats haven’t coalesced around a plan to pick a replacement nominee.

Other Democrats have rallied around Biden, with varying levels of forcefulness. Rep. Steven Horsford (D., Nev.), chair of the Congressional Black Caucus, said Monday: “Biden is the nominee…we’re not going back, we’re moving forward.” Rep. Frederica Wilson (D., Fla.) said Sunday that “any ‘leader’ calling for President Biden to drop out needs to get their priorities straight and stop undermining this incredible actual leader.”

Democrats know they are up against a clock should they choose to act, with the Democratic National Convention set for August in Chicago, when they are set to formally nominate Biden as president. Rep. Jim Clyburn (D., S.C.)—an influential voice who helped Biden win the Democratic nomination in 2020—has begun floating ideas for how to determine a new candidate, should Biden step aside, through what he has characterized as a “mini primary.”

Biden is in the driver’s seat headed into the convention, having won almost all of the delegates. Party rules say delegates pledged to a candidate “shall in all good conscience reflect the sentiments of those who elected them.” Biden’s critics have been pushing him to step aside voluntarily, seeing the chances of a majority of delegates defying their pledge to Biden as remote.

Biden argued in his letter that the debate over his future was hurting Democrats’ chances against Trump. “The question of how to move forward has been well-aired for over a week now,” he wrote. “And it’s time for it to end. We have one job. And that is to beat Donald Trump.” He added: “Any weakening of resolve or lack of clarity about the task ahead only helps Trump and hurts us.”

First lady Jill Biden was making the case for her husband during stops in North Carolina, Florida and Georgia. “For all the talk out there about this race, Joe has made it clear that he’s all in,” the first lady said during an event with veterans and military families in Wilmington, N.C.

Emily Glazer and Rebecca Ballhaus contributed to this article.