Representative Hakeem Jeffries, Democrat of New York and the minority leader, has scheduled a virtual meeting on Sunday with senior House Democrats to discuss President Biden’s candidacy and the path forward, according to a senior official familiar with the plan.

The session, which is to include the ranking members of congressional committees who make up the top echelons of the party in the House, comes at a time of profound worry among Democrats on Capitol Hill about Mr. Biden’s poor performance at last week’s presidential debate. House Democrats have not met as a group since, even as concerns have mounted about Mr. Biden’s viability as a candidate and the impact he could have on his party’s ability to win back control of the chamber and hold the Senate should he remain in the race.

Mr. Jeffries has been in listening mode all week, refraining from pressuring Democrats to rally around the president but also encouraging them not to be rash in their public pronouncements as Mr. Biden and his team determine the best path forward.

But Democrats have begun to splinter. Four in the House — Representatives Lloyd Doggett of Texas, Raúl Grijalva of Arizona, Seth Moulton of Massachusetts and Mike Quigley of Illinois — have called for the president to withdraw, while others have made public their serious concerns about his ability to prevail in the race.

On Friday, Mr. Quigley said he had had a “hard time” getting to the point of urging the president to get out of the race.

But, he told MSNBC, “clearly, the alternative now is a very bleak scenario with, I would say, almost no hope of succeeding — and it doesn’t just affect the White House. It affects all of Congress and our future.”

Senator Mark Warner, Democrat of Virginia, has been working to organize a meeting of Democrats in his chamber to discuss their concerns about Mr. Biden’s candidacy and what should be done, according to multiple people with direct knowledge of the effort who spoke about it on the condition of anonymity.