Speaker Pelosi, a very influential figure in the Democratic Party on Capitol Hill, appeared to ignore Biden’s insistence on moving forward on Wednesday.
Asked whether she should continue to run for office, she told MSNBC's Morning Joe: “I hope I go with whatever he decides to do.
“It's up to the president whether he runs or not. We're all encouraging him to make that decision, because time is running out.”
Pelosi acknowledged that the president had made a request at the NATO summit, telling MSNBC: “I told everybody, 'Let's just wait a minute.'
“Whatever you think, tell someone in secret, but you don't have to put it out there until we see what happens this week. But I'm very proud of the president.”
About a dozen Democratic elected officials have suggested Trump drop out of his campaign following his June 27 debate.
On Tuesday, Colorado Senator Michael Bennet became the first Democratic senator to publicly oppose the bill.
He stopped short of calling for Biden to resign outright, but said Trump would win the election in a “landmark.”
Soon after, Vermont Senator Peter Welch wrote in the Washington Post, “In the interest of our country, I urge President Biden to withdraw from the race.”
New York Rep. Pat Ryan later wrote on X: “For the good of our country, and for the good of my two young children, I am calling on Joe Biden to step down.”
And Connecticut Democratic Senator Richard Blumenthal told reporters he had “deep concerns” about Mr Biden’s ability to win the election.
The Biden campaign repeated the president's statement that “we will fight this race to the end.”
House Minority Leader Hakeem Jeffries, D-Calif., plans to speak with President Biden by Friday to discuss concerns raised by several lawmakers.
But overall, support among elected Democrats remains strong.
California Gov. Gavin Newsom, whom Clooney had named as a potential replacement, said he still supports Mr. Biden.
The Congressional Black Caucus, a group of about 60 politicians, and progressive House members like Alexandria Ocasio-Cortez have publicly supported Mr. Biden.
On Tuesday, Senate Democratic leader Chuck Schumer said, “I’m with Joe.” But Axios reported that Schumer had privately told donors that he was willing to dump Biden.
In interviews with CBS News (the BBC's US partner), two unnamed senior Democratic officials said there had been a “convergence” of opinion among elected Democrats, donors and groups that support the president's party in the past 24 hours.
One source said all stakeholders had reached “pretty much a consensus” on what Mr Biden should do.
Questions were also raised about the Democratic campaign at the NATO summit in Washington, D.C.
