It is reminiscent of how Black Democrats rallied behind Mr. Biden to help propel him to his primary victory in 2020. It also speaks to a broader racial and generational divide in the party that could be consequential in determining how it moves forward from the president’s current crisis.

More than a dozen Black Democrats in both the House and Senate have begun to offer a strong defense of him, even as their colleagues whisper in increasingly urgent tones about pushing him aside.

“The choice for American leadership and our democracy is clear,” Representative Joyce Beatty of Ohio, a former chairwoman of the Black Caucus, said in a social media post late Sunday in which she lauded Mr. Biden’s record as a defender of democracy.

“I don’t care what anybody says — it ain’t going to be no other Democratic candidate,” Representative Maxine Waters of California told audiences at the Essence festival in New Orleans over the weekend. “It’s going to be Biden.”

Ms. Waters was also one of the few top Democrats who spoke up for the president during a high-level virtual meeting on Sunday in which several ranking members of key committees privately said he needed to withdraw from the race, according to people who attended and were briefed on the session. Representative David Scott of Georgia, another senior member of the Black Caucus, also spoke in favor of Mr. Biden, the people said.

Representative James E. Clyburn, Democrat of South Carolina and the co-chairman of Mr. Biden’s re-election campaign, continues to be one of his most prominent supporters and has also pushed back against calls for the president to resign.

“Joe Biden is who our country needs, and his presidency has laid a foundation upon which we can continue our pursuit of a more perfect union,” he said in a social media post on Friday. Mr. Clyburn’s endorsement four years ago is often credited with helping Mr. Biden prevail in the South Carolina presidential primary and propelling him to win his first term.

Mr. Clyburn caused some hand-wringing among Democrats last week when he discussed the possibility of a “mini-primary“ to replace Mr. Biden before the Democratic National Convention next month should he withdraw from the race. But he quickly moved to clarify that he considered the idea strictly hypothetical.

Younger Black lawmakers have been slower to offer their backing for Mr. Biden, staying mostly silent so far. And the highest-ranking Black Democrat in Congress, Representative Hakeem Jeffries of New York, the minority leader, has stayed quieter. Days after the debate last month, he said Mr. Biden was poised to make a “comeback” after an “underwhelming” performance.

“The reality is Joe Biden has confronted and had to come back from tragedy, from trials, from tribulations throughout his entire life,” Mr. Jeffries said during an interview with MSNBC. “So the moment that we’re in right now is a comeback moment.”

But Mr. Jeffries has done little since then to tamp down on what appears to be a groundswell of sentiment within his ranks in favor of replacing Mr. Biden at the top of the ticket. He did not speak up during the high-level private meeting on Sunday — which was billed as a listening session — to try to defend the president or rally Democrats around salvaging his candidacy, and he gave no indication to lawmakers about whether he believed Mr. Biden should continue in the race.

The Biden campaign has taken solace in the backing of Black Democrats, an influential force on Capitol Hill and in the party, at an otherwise grim time. It chose a Black church in Philadelphia as the backdrop on Sunday for Mr. Biden to make his case.

“You know I’ve been doing this a long time, and I’ve honest to God never been more optimistic about America’s future — if we stick together,” Mr. Biden told the congregation at Mount Airy Church of God in Christ in Philadelphia.