President Joe Biden insisted again Monday he would not quit the US election race, as the White House denied he had Parkinson's disease following a disastrous debate performance.

The 81-year-old dared Democratic critics to either challenge him at next month's party convention in Chicago or back him against Donald Trump in November's vote, reports CNN. The president lashed out in both a letter to Congress and a rare call to a television programme, at the start of a critical week that includes a NATO summit in Washington where he will face fresh scrutiny.

"I am firmly committed to staying in the race," Biden wrote in the letter. "It is time to come together, move forward as a unified party and defeat Donald Trump," he said. "It's time for it to end." The embattled president followed up by phoning into MSNBC's "Morning Joe" television program to say he was "getting so frustrated by the elites" in the party. "Any of these guys that don't think I should run -- run against me. Announce for president, challenge me at the convention," he added. But even as he doubled down, the pressure mounted on the oldest president in US history.

Congressman Adam Smith, the senior Democrat on the US House Armed Services Committee, said Biden should step aside. "I think it's become clear he's not the best person to carry the Democratic message," he said.