"I am not going anywhere," Biden told MSNBC after calling into the network's Morning Joe program.
He urged anyone who wants him to step aside to "challenge me" when the Democratic National Convention meets in August.
The interview was another example of Biden trying to recover from a shaky debate outing against Republican Donald Trump on June 27 that raised questions about his mental fitness.
Biden expressed frustration with what he called an effort by "elites" to force him out of the presidential race against Trump, whom he defeated in 2020, with the election coming up on November 5.
When Morning Joe co-host Mika Brzezinski ticked off a list of major news organisations and pundits who have called on him to step aside, Biden brushed off the question.
"I don't care what those big names think," Biden said.
US President Joe Biden says there has been enough speculation and "it's time for it to end". (AP PHOTO)
"The bottom line here is that I'm not going anywhere. I am not going anywhere. I wouldn't be running if I didn't absolutely believe that I am the best candidate to beat Donald Trump in 2024."
Earlier on Monday, Biden told his fellow Democrats in Congress that he is "firmly committed" to his re-election campaign.
"I want you to know that despite all the speculation in the press and elsewhere, I am firmly committed to staying in this race, to running this race to the end, and to beating Donald Trump," Biden wrote politicians as they returned to Washington DC following the July 4 recess.
Biden wrote in the two-page letter that "the question of how to move forward has been well-aired for over a week now. And it's time for it to end".
He stressed that the party has "one job," which was to defeat presumptive Republican presidential nominee Donald Trump in November.
Democrats face an uphill battle defending their 51-49 US Senate majority, with incumbents up for re-election in multiple Republican-leaning states, and some in the party view recapturing a House majority as their best chance of keeping a hold on one of the levers of power in Washington DC should Trump win back the White House he lost to Biden in 2020.
Biden will go on meeting voters at churches, union halls and other venues in coming days, administration officials said.
At the same time he plans to reach out to lawmakers he has known for decades, they said, as he tries to calm concerns.
Several congressional Democrats have called for him to drop out.
Senator Dick Durbin, the chamber's No. 2 Democrat, told reporters Biden's candidacy "will be thoroughly discussed this week, as it should".
He said he had spoken with about a dozen of his colleagues, who held a range of views.
"The American public is very concerned about his ability to continue to serve as commander in chief, and he's going to have to do more to persuade them than simply writing a letter to Congress," Democratic Representative Joe Morelle told reporters.
Biden's halting debate performance has prompted some to question whether he was suffering from a neurological disorder such as Parkinson's disease, which can cause slurred speech and halting movement.
White House spokeswoman Karine Jean-Pierre said Biden was evaluated and given a clean bill of health in February and is not being treated for the disease.
Biden's doctor has said further testing is not warranted, she said.
Although Biden has secured enough delegates to win the Democratic presidential nomination, some donors and lawmakers have called for him to step aside and let Vice President Kamala Harris or another candidate lead the ticket.
with AP
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