Biden's letter seeks to quell a revolt brewing among Democratic lawmakers.

Four senior members of the House of Representatives - Jerry Nadler, Adam Smith, Mark Takano and Joe Morelle - on Monday joined growing calls for him to resign, bringing the total to nine.

Senate Democrats will meet later in the day to discuss Biden's candidacy later Monday, as called by Mark Warner.

Partisan unrest entered its second week on Monday, at the same time NATO leaders gather here in Washington DC for their annual summit.

The allies will be keeping an eye on the embattled US president's internal problems as they discuss the threats posed individually and collectively as a group by Russia, China and Iran.

The Democratic Party has been divided by a bitter debate sparked by his weak performance in the first presidential debate against former President Donald Trump, the presumptive Republican nominee, on June 27.

Some Democrats believe he not only seemed unable to defeat Trump in the election, but also to govern the country for the next four years, if he wins a second term. They have asked him to make way for someone younger and healthier.

Vice President Kamala Harris is a leading contender.

But President Biden isn't going anywhere.

"Despite all the speculation in the press and elsewhere, I am firmly committed to staying in this race, running it to the end, and defeating Donald Trump," he wrote in the letter.

"The question of how to move forward has been well-posed for more than a week. And it is time for it to end."

In a call to a morning talk show, Biden issued a challenge to "party elites" who have been calling for his ouster to compete against him for the party nomination at the Chicago convention.

"I'm getting so frustrated with the elites, I'm not talking about you, but the party elite, who...know a lot more," Biden said, adding "challenge me at the convention."

Biden reminded lawmakers in the letter that he won the party's nomination with 14 million votes, which represented 87 percent of the votes cast, and won nearly 3,000 party delegates (who will formally choose the nominee at the convention).

"This was an open process to anyone who wanted to run. Only three people chose to challenge me. One did so poorly that he dropped out of the primary to run as an independent. Another attacked me for being too old and was soundly defeated. Democratic Party voters have voted and have chosen me as the party's candidate," he wrote.

"Now we just say this process didn't matter? That voters don't have a say? I refuse to do that."