President Biden has become more receptive in the last several days to hearing arguments about why he should drop his re-election bid, Democrats briefed on his conversations said on Wednesday, after his party’s two top leaders in Congress privately told him they were deeply concerned about his prospects.

Mr. Biden has not given any indication that he is changing his mind about staying in the race, the Democrats said, but has been willing to listen to rundowns of new and worrying polling data and has asked questions about how Vice President Kamala Harris could win.

The accounts suggest that Mr. Biden, privately at least, is striking a more open-minded posture than he did last week when he lashed out at a number of House Democrats who pressed him to step aside.

One person close to the president said that it would be wrong to call him receptive to the idea of dropping out but that he “is willing to listen.” But this person emphasized there was no sign that Mr. Biden was changing course at this point.

The descriptions emerged after Senator Chuck Schumer and Representative Hakeem Jeffries, the two top Democrats in Congress, each told Mr. Biden privately over the past week that their members were deeply concerned about his chances in November and the fates of House and Senate candidates should he remain at the top of the ticket, according to two people briefed on the conversations.

The White House suggested that Mr. Biden was unmoved by their discussions.

“The president told both leaders he is the nominee of the party, he plans to win and looks forward to working with both of them to pass his 100 days agenda to help working families,” said Andrew Bates, a White House spokesman.