Boris Johnson asked government scientists whether people could kill Covid by using a "special hair dryer" up their nose, his former aide has claimed.
Dominic Cummings said the former prime minister shared a video of a man using such a device with his top advisers Sir Patrick Vallance and Sir Chris Whitty.
He then asked the medical experts what they thought about the clip, he added.
Mr Johnson has been approached for a comment.
The eye-catching claim was among several made by Mr Cummings in his witness statement to the inquiry into the government's pandemic response.
Mr Cummings was Mr Johnson's chief adviser until he left Downing Street in late 2020 after an internal battle over his role. He has since been a vocal critic of the former prime minister's leadership during the response to the virus.
In his statement, Mr Cummings said the former prime minister "did not want us to 'antagonise' the media by calling out false stories". Staff, he wrote, were even unsure whether "he was not himself the source of false stories".
"A low point was when he circulated a video of a guy blowing a special hair dryer up his nose 'to kill Covid'," he wrote.
He said Mr Johnson shared the Youtube clip - since deleted - in a WhatsApp group with Sir Chris, England's chief medical officer (CMO), and Sir Patrick, then the government's chief scientific adviser (CSA).
He then "asked the CSA and CMO what they thought", he added. The statement does not detail what response - if any - was given by the advisers.
Elsewhere in his witness statement, Mr Cummings alleged that the former prime minister asked him to find a "dead cat" (a term for a striking claim used to distract the media) to draw attention away from Covid in late 2020.
In the summer of that year, he wrote, Mr Johnson "wanted to declare Covid 'over' even though this would obviously backfire".
"At one point in autumn he told me to 'put your campaign head back on and figure out how we dead-cat Covid, I'm sick of Covid, I want it off the front pages,'" Mr Cummings added.
"I said that no campaign could 'dead-cat Covid' and I would not spend my time on such a project," he added.
Mr Cummings is one of several senior government advisers and officials to have submitted evidence to the Covid inquiry this week.
In her witness statement, former deputy cabinet secretary Helen MacNamara suggested officials sought to obscure how seriously ill Mr Johnson had become after he was admitted to hospital with Covid in April 2020.
Ms MacNamara said lines journalists were told about Mr Johnson "receiving updates in hospital" and "continuing to receive a box" were "technically accurate but right on the edge of what was comfortable".
Ms MacNamara said senior press advisers had warned against saying something "untrue" but it was "fair to say that the lines used allowed for a more positive impression of the prime minister's health at that point".
"The prime minister was conscious, and it was possible to contact him and for him to make decisions but he was very ill."