A bad-tempered and unedifying US presidential debate between the two oldest candidates ever to run for office degenerated into a squabble over golfing prowess on Thursday.

The first head-to-head in an already painfully long campaign saw 81-year-old Joe Biden and his 78-year-old challenger Donald Trump trade insults and accusations for 90 minutes on prime time television.

There was name-calling: "You're the worst!" "No, YOU'RE the worst!"

There were accusations: "You're a whiner!"

And then they fought over their golf handicaps.

"He can't hit a ball 50 yards," said Trump, on one of the few occasions the two men directly addressed each other.

"He challenged me to a golf match. He can't hit a ball 50 yards."

Trump's own vitality was never in question, he boasted, insisting "I'm in as good a shape as I was years ago."

Not to be outdone over his putting prowess, Biden insisted he was game on the green.

"I'd be happy to have a driving contest," he said. "I got my handicap when I was the vice president down to a six."

Trump scoffed.

"A six handicap?" he snorted. "I've seen your swing. I know your swing."

The exchange came towards the end of the CNN-hosted debate, which had started without the handshake that is customary on such occasions and gone downhill from there.

The animosity between the two men was palpable, with Biden taking an early swing at a man he said had "the morals of an alley cat."

"How many billions of dollars do you owe in civil penalties for molesting a woman in public... for having sex with a porn star... while your wife was pregnant," he said, in reference to Trump's alleged dalliance with adult film actress Stormy Daniels.

The Republican former president again denied adultery, but a New York jury found him guilty of 34 counts of falsifying business records to cover up hush-money payments to her.

Trump wasted few chances to hammer home his claim that Biden was "weak" and not "a leader."

He also took aim at Biden's perceived mental frailties, an issue that polls repeatedly show voters are concerned about.

"I took two tests, cognitive tests. I aced them, both of them, as you know, we made it public," he said.

"He took none. I'd like to see him take one, just one, a real easy one, like go through the first five questions. He couldn't do it."