White House spokeswoman Karine Jean-Pierre rejected those reports outright, insisting Mr. Biden has no intention of withdrawing.
Mr. Biden told a call with campaign and party staffers that he is going nowhere.
Mr. Walz said Mr. Biden was "fit to serve."
Netflix co-founder Reed Hastings, one of the Democratic Party's biggest donors, told the New York Times that Biden should withdraw.
Arizona congressman Raul Grijalva became the second sitting Democrat to call on Mr. Biden to drop out.
Joe Biden is "absolutely not" pulling out of the U.S. presidential race, his spokeswoman said on July 3, as pressure mounted following his disastrous debate performance against Donald Trump.
Panic has gripped his Democratic Party in the wake of last week's TV debate, and internal rumblings about finding a replacement candidate before November's election have been amplified by polls showing Mr. Trump extending his lead.
The New York Times and CNN reported that Mr. Biden, 81, had acknowledged to a key ally that his reelection bid was on the line if he failed to quickly reassure the public that he was still up to the job.
White House spokeswoman Karine Jean-Pierre rejected those reports outright, insisting Mr. Biden has no intention of withdrawing.
"The President is clear-eyed and he is staying in the race," she told reporters.
Mr. Biden told a call with campaign and party staffers that he is going nowhere.
"I'm in this race to the end and we're going to win because when Democrats unite, we will always win. Just as we beat Donald Trump in 2020, we're going to beat him again in 2024," he said, according to a source close to the campaign.
He repeated that message in an emergency meeting with Democratic governors, who pledged their continued support, attendees said afterward.
"As the President continued to tell us, and show us, that he was all in... we said that we would stand with him," Maryland Governor Wes Moore, seen as a rising star and potential future presidential candidate, told reporters alongside Minnesota's Tim Walz and Kathy Hochul of New York.
Mr. Walz said Mr. Biden was "fit to serve."
Michigan Governor Gretchen Whitmer, who also attended the meeting at the White House and is seen as one of the top picks to replace Mr. Biden if he should drop out, said on social media platform X that "he is in it to win it and I support him."
Mr. Biden has admitted he performed poorly in the debate, and was blunt in a radio interview recorded Wednesday with Wisconsin's Civic Media.
"I screwed up. I made a mistake. That's 90 minutes on stage. Look at what I've done in 3.5 years," he said.
He echoed that sentiment in an interview with Pennsylvania's WURD radio on Thursday, saying "I had a bad debate."
Aftermath
The Biden campaign has been desperate to reassure Democratic donors and voters that the president's performance against Trump was a one-off.
But party figures have voiced bafflement over what they see as deflection and excuses from the President and his aides.
Netflix co-founder Reed Hastings, one of the Democratic Party's biggest donors, told the New York Times that Biden should withdraw.
"Mr. Biden needs to step aside to allow a vigorous Democratic leader to beat Mr. Trump and keep us safe and prosperous," he said in an email to the paper.
The concern was compounded by a New York Times poll conducted after the debate that showed Trump with his biggest lead ever over Mr. Biden — 49% to 43% of likely voters.
It wasn't until Wednesday — six days after the debate — that Mr. Biden completed a round of calls with Democratic congressional leaders, and staffers have also voiced consternation over the glacial pace of the outreach.
"We are getting to the point where it may not have been the debate that did him in, but the aftermath of how they've handled it," a senior Democratic operative told Washington political outlet Axios.
Mr. Biden may be tested on his ability to think on his feet when he sits with ABC News on Friday for his first television interview since the debate, and he will also hit the swing states of Wisconsin and Pennsylvania in the coming days.
'More worrisome'
The President has cited fatigue as a new explanation for his poor debate showing, saying that he was unwise to travel "around the world a couple times" before the debate.
But he had been back in the United States for nearly two weeks and spent two days relaxing and six days preparing before the debate.
Democratic lawmakers have begun to go public with their doubts. Arizona congressman Raul Grijalva became the second sitting Democrat to call on Mr. Biden to drop out.
"If he's the candidate, I'm going to support him, but I think that this is an opportunity to look elsewhere," Grijalva said, according to the Times.
In the street where the president grew up in Scranton, Pennsylvania, there was sympathy for Mr. Biden — but no campaign signs for either candidate.
"I was embarrassed for him. I felt he didn't feel well and he probably shouldn't have gone on the stage," said 73-year-old Jamie Hayes.