President Biden said in a letter to congressional Democrats on Monday that he is “firmly committed to staying in the race,” a defiant answer to allies on Capitol Hill who have said in recent days that he should drop out.

“The question of how we move forward has been well aired for over a week now,” Mr. Biden wrote in the two-page letter, released by his campaign. “And it’s time for it to end. We have one job. And that is to beat Donald Trump.”

The letter comes just a day after five senior House Democrats said during a private conference call that they believe Mr. Biden must step down from the race, adding enormous pressure on the president and his advisers.

But the president repeated in the letter that he does not agree with the arguments being made against him. And he said those trying to push him out of the race would be denying the wishes of the voters who participated in the primary process.

“Do we now say this process doesn’t matter?” he wrote.