US President Donald Trump demanded on Sunday that his Democratic rival, Joe Biden, take a drug test either before or after the pair's first debate on Tuesday, in his latest salvo against his opponent's mental acuity.

“I will be strongly demanding a Drug Test of Sleepy Joe Biden prior to, or after, the Debate on Tuesday night,” Trump tweeted.

“Naturally, I will agree to take one also. His Debate performances have been record setting UNEVEN, to put it mildly. Only drugs could have caused this discrepancy???” he continued, without offering any evidence for the claim.

According to US media reports, on Saturday their teams finalised the conditions for the debate, to be moderated by Fox News reporter Chris Wallace, including forgoing the traditional handshake and with only a small audience due to Covid-19 restrictions.

The condition of a drugs test was not mentioned.

Both septuagenarians are prone to blunders and gaffes when speaking.

But the 74-year-old Trump has spent months denigrating 77-year-old Biden's mental state, and suggested several times in recent weeks without any evidence that the former vice president may be using unspecified drugs to boost his performance.

For the most part Biden has shrugged off the accusations, calling for voters to observe the two men together.

“Watch me. Look at us both,” he said in an August interview with ABC.

On Saturday Biden said he expects “personal attacks and lies” from the president during the debate, likening Trump to Nazi propaganda chief Joseph Goebbels.

Tuesday's clash in Cleveland, Ohio, the first of three 90-minute debates, represents the first time voters will have the chance to see the candidates facing off against one another directly.