US President Joe Biden and his would-be challenger Donald Trump have been attacking one another as the 2024 White House campaign heats up.
Mr Biden said part of his motivation to run for a second term next year is to thwart the Republican, adding that "we cannot let him win".
In a Fox News event, Mr Trump said he thought Mr Biden was too old for such a political rematch.
Neither candidate is yet the official nominee of their respective party.
Mr Trump is the runaway front-runner in the Republican race even as he faces four criminal cases. Mr Biden, as the incumbent president, is the presumptive Democratic nominee.
Current opinion polls indicate a hypothetically tight race between the two.
Speaking to reporters off camera at a campaign fundraising event near Boston, Mr Biden said: "If Trump wasn't running, I'm not sure I'd be running. But we cannot let him win."
The president's remarks were regarded as the first time he has pinned his aspirations for a second term squarely on opposing Mr Trump's comeback bid.
Later on Tuesday, Mr Trump appeared at a televised Fox News town hall in Davenport, Iowa.
The host, Sean Hannity, asked: "You are promising America tonight, you would never abuse power as retribution against anybody?"
"Except for day one," Mr Trump replied. "I want to close the border and I want to drill, drill, drill."
He also said he did not think Mr Biden would "make it physically" through the gruelling campaign ahead.
His rival's mental state, he said, is "possibly equally as bad or even worse" than his physical state.
Mr Trump is skipping the fourth Republican presidential debate on Wednesday, which will be held in Alabama.