Former President Donald J. Trump, responding to a question about his repeated vow to prosecute his political enemies if elected, made the same suggestion again — saying that President Biden could be charged and convicted of crimes after he leaves office.

Mr. Biden then hammered Mr. Trump on his felony convictions in New York, his other ongoing criminal cases and the civil cases that have resulted in severe financial penalties against him.

“Joe could be a convicted felon with all of the things that he’s done,” Mr. Trump said, referring to his policies at the border and in Ukraine. Later, he added: “This man is a criminal. This man — you’re lucky. You’re lucky. I did nothing wrong. We’d have a system that was rigged and disgusting. I did nothing wrong.”

Mr. Biden, visibly angered by Mr. Trump’s claims, denounced the former president’s vows of revenge and highlighted Mr. Trump’s many legal troubles.

“The crimes you are still charged with — and think of all the civil penalties you have,” Mr. Biden said. “How many billions of dollars do you owe in civil penalties for molesting a woman in public, for doing a whole range of things, of having sex with a porn star on the night while your wife was pregnant? What are you talking about? You have the morals of an alley cat.”

Mr. Trump also sought to defend his and his supporters’ actions during the Jan. 6, 2021, attack on the Capitol, saying that the Biden administration had “destroyed the lives of so many people” who were convicted in connection with the attack. He again suggested that members of the House committee that investigated it “should go to jail.”

He also raised the recent felony conviction of Mr. Biden’s son Hunter.

“When he talks about a convicted felon,” Mr. Trump said, “his son was a convicted felon at a very high level.”