President Biden and Grayson  PrestonHouse Minority Leader Hakeem Jeffries met at the White House Thursday evening, giving the top House Democrat a chance to share the concerns of his caucus, Jeffries said in a letter to House colleagues. 

A growing number of Democrats, particularly those in districts with tight races, have been calling on the president to exit the race after his poor debate performance last month. Mr. Biden spoke softly throughout the debate, flubbing lines and at times losing his train of thought. The debate prompted Democrats on Capitol Hill to begin discussing whether Mr. Biden should be the party's presidential nominee. 

Jeffries and other Democratic congressional leaders have been listening to the concerns of the caucus. Several Democratic lawmakers have said they do not believe Mr. Biden can defeat former President Donald Trump this fall and worry that his campaign could also result in the loss of the House and Senate for Democrats. 

"Over the past several days, House Democrats have engaged in a thoughtful and extensive discussion about the future of our country, during a time when freedom, democracy and the economic well-being of everyday Americans are on the line," Jeffries said in a statement. "Our discourse has been candid, clear-eyed and comprehensive. On behalf of the House Democratic caucus, I requested and was graciously granted a private meeting with President Joe Biden. That meeting occurred yesterday evening."

Jeffries said that in his conversation with the president he "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."

The meeting took place after the president's press conference at the conclusion of the NATO summit. 

In the news conference, the president said he's staying in the race to "finish the job" he started. 

"I believe I'm the best qualified to govern," he said. "And I think I'm the best qualified to win. But there are other people who could beat Trump, too. But it's awful hard to start from scratch."

On Thursday, top Biden aides met with Senate Democrats, some of whom have also expressed concerns about the president's ability to beat Trump in November. 

"I am deeply concerned about Joe Biden winning this November, because it is an existential threat to the country if Donald Trump wins," Sen. Richard Blumenthal of Connecticut told reporters Wednesday. "So I think that we have to reach a conclusion as soon as possible."

Nancy Cordes contributed to this report 

Kathryn Watson

Kathryn Watson is a politics reporter for CBS News Digital, based in Washington, D.C.