A group of leading Democratic governors offered words of support for Joe Biden on Wednesday as pressure mounted on the president to leave the race.

The governors, including Tim Walz of Minnesota, Wes Moore of Maryland, Gavin Newsom of California and Kathy Hochul of New York, held a closed-door meeting with Biden in Washington as he sought to reassure his party – and the public – that he is up to the job after a shaky debate performance.

Related: Biden says ‘I’m not leaving’ as cracks appear in Democrats’ support

Biden met for more than an hour at the White House in person and virtually with more than 20 governors from his party. The governors told reporters afterward that the conversation was “candid” and said they expressed concerns about Biden’s debate performance last week. They reiterated that defeating Donald Trump in November was the priority, but said they were still standing behind Biden and did not join other Democrats who have been urging him to withdraw his candidacy.

“We, like many Americans, are worried,” Walz of Minnesota said. “We are all looking for the path to win – all the governors agree with that. President Biden agrees with that. He has had our backs through Covid … the governors have his back. We’re working together just to make very, very clear that a path to victory in November is the No 1 priority and that’s the No 1 priority of the president … The feedback was good. The conversation was honest.”

“The president is our nominee. The president is our party leader,” added Moore of Maryland. He said Biden “was very clear that he’s in this to win it”.

“We were honest about the feedback we’re getting … and the concerns we’re hearing from people,” Moore said. “We’re going to have his back … the results we’ve been able to see under this administration have been undeniable.”

The meeting capped a tumultuous day for Biden as members of his own party, and a major democratic donor, urged him to step aside amid questions over his fitness for office. Two Democratic lawmakers have called on Biden to exit the race, and a third Congressman said he had “grave concerns” about Biden’s ability to beat Trump. The White House, meanwhile, was forced to deny reports that Biden is weighing whether his candidacy is still viable.

Biden, for his part, has forcefully insisted that he is staying in the race.

“Let me say this as clearly as I possibly can, as simply and straightforward as I can: I am running … no one’s pushing me out,” Biden said on a call with staffers from his re-election campaign. “I’m not leaving. I’m in this race to the end and we’re going to win.”

Kamala Harris has also stood by his side, despite some insiders reportedly rallying around her as a possible replacement. “We will not back down. We will follow our president’s lead,” the vice-president reportedly told staffers on Wednesday.

Related: Kamala Harris: insiders rally behind VP to replace Biden if he bows out

Michigan governor Gretchen Whitmer also threw her support behind Biden. “He is in it to win it and I support him,” she said on Twitter/X after the meeting.

Whitmer is one of several Democratic governors who have been cited as possible replacements if Biden were to withdraw his candidacy. Gavin Newsom, whose name has also been floated, flew in for the governors’ meeting on Wednesday, saying afterwards: “I heard three words from the president tonight – he’s all in. And so am I.”

Newsom has been a top surrogate for Biden’s re-election campaign, but has also garnered increasing buzz as a potential replacement if Biden were to withdraw. He was swarmed by reporters after the debate ended last week, some asking him if he’d replace Biden.

The Associated Press contributed reporting