Jill Biden declared herself “all in” on President Joe Biden’s bid to remain as the presumptive Democratic presidential nominee, despite calls by some Democrats for him to drop out after his damaging debate performance against Donald Trump shook their confidence in him.

The president himself has brushed aside those calls and insisted anew that he isn’t leaving the race.

“For all the talk out there about this race, Joe has made it clear that he’s all in,” the first lady told a military crowd in Wilmington, North Carolina, the first of three battleground states she was visiting.

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President Joe Biden and first lady Jill Biden (AP Photo/Manuel Balce Ceneta)

“That’s the decision that he’s made, and just as he has always supported my career, I am all in too,” said Jill Biden, who teaches English and writing as a community college professor.

Her day-long tour was part of the Biden campaign’s broader effort to rebound from the president’s halting performance against Mr Trump in last month’s debate.

The debate led some congressional Democrats and others to call on him to let another candidate challenge Mr Trump because they no longer believe the 81-year-old president is mentally and physically capable of defeating the former Republican president in November.

The president has insisted since the debate that he is staying in the race. He did so again on Monday in a letter to congressional Democrats and during an on-air telephone interview with MSNBC.

The first lady then used her appearance to draw contrasts between her husband’s and Mr Trump’s attitudes toward US service members, veterans and their families.

The president’s late son Beau served in Iraq as a member of the Delaware Army National Guard, and the first lady’s father was a Navy signalman during World War II.

“This is personal to us,” she said, describing the waits to connect phone calls with a service member stationed overseas or having to smile through a loved one’s absence on holidays.

“Let me ask you this … Does Donald Trump know what it’s like?” she said.

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The president has faced calls to step aside following a poor performance in the first debate against Donald Trump (AP Photo/Gerald Herbert, File)

The first lady mentioned reports that Mr Trump, during a 2018 trip to France, referred to service members who paid the ultimate sacrifice as “suckers” and “losers”/

Mr Trump denies making the comments.

“It’s disgraceful, but it’s not surprising,” she said.

Noting that the Supreme Court has said presidents are immune from prosecution for acts committed while in office, the first lady said “our democracy cannot withstand a Trump president with virtually no limits”.

“Members of our military honour their oath to support and defend the Constitution. We cannot trust Donald Trump to do the same,” she said. “You deserve a commander in chief who serves with integrity and wisdom and character, and that’s my husband, Joe Biden.”

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Joe Biden and Donald Trump clashed over who cares the most about veterans during their debate in June (AP Photo/Evan Vucci)

A spokesperson for Mr Trump’s campaign did not immediately respond to requests for comment.

During the debate, Mr Biden and Mr Trump argued over who cares the most about veterans.

Mr Biden noted that he recently visited an American military cemetery in France, the final resting place for US soldiers who fought in the First World War, which Mr Trump notably skipped on his 2018 trip.

Mr Trump asserted during the debate that the Democratic president is coddling migrants while neglecting the needs of veterans and service members, and he faulted Mr Biden for the chaotic withdrawal of US troops from Afghanistan.