Democrat presidential candidate Joe Biden has said the second televised debate should not take place if President Donald Trump is still infected.
"I think if he still has Covid, we shouldn't have a debate," Biden said on Tuesday.
"I think we're gonna have to follow very strict guidelines. Too many people have been infected and it's a very serious problem."
The debate is scheduled for 15 October in Miami, Florida.
Trump tested positive on Thursday 1 October, but it's not clear when he caught the virus or began to feel unwell.
According to US public health guidelines, Trump should remain in isolation for up to 10 days after symptoms first appear.
Biden sentiments come after Covid-19 is spreading further among those around US President Donald Trump, with White House adviser Stephen Miller and a top military official infected.
Mr Miller, who has been self-isolating for the past five days, confirmed he had contracted coronavirus on Tuesday.
Top US General Mark Milley and other military leaders are also quarantining after Coast Guard official Admiral Charles Ray tested positive.
Other officials are self-isolating "out of an abundance of caution".
In a statement, Mr Miller said he had been "testing negative every day" until Tuesday, adding that he was now in quarantine.
His wife, Katie Miller, who is Vice-President Mike Pence's spokeswoman, contracted the virus back in May and later recovered.
In July, Mr Miller's 97-year-old grandmother, Ruth Glosser, reportedly died due to complications with Covid-19.
The White House denied that coronavirus had caused Mrs Glosser's death, saying in a statement she "died peacefully in her sleep from old age".
But Mr Miller's uncle produced a death certificate listing "respiratory arrest" and Covid-19 as "a condition leading" to the cause of Mrs Glosser's death.
Mr Miller - who writes the president's speeches - is known for his hardline views on immigration.
ince President Trump tested positive last week, a number of senior Republicans and others close to him have been confirmed as having the virus.
This includes First Lady Melania Trump, aide Hope Hicks, and a number of Republican senators.
Press Secretary Kayleigh McEnany has tested positive, announcing her diagnosis on Monday, and three other members of staff in the press office - Chad Gilmartin, Karoline Leavitt and Jalen Drummond - have also tested positive.
Ms McEnany was seen speaking to journalists without wearing a mask on Sunday but said no members of the press had been listed as close contacts by the White House medical unit.
Many of the people in Mr Trump's inner circle who have tested positive attended a gathering at the White House Rose Garden on 26 September that is being scrutinised as a possible "super-spreader event".
Another coronavirus case to emerge from that event, at which the president unveiled his nominee for the US Supreme Court, is a Christian minister from California.
Pastor Greg Laurie, who is said to have mild symptoms, was also with US Vice-President Mike Pence earlier in that day at a prayer march in central Washington DC.
Plexiglass will be used to separate Vice-President Mike Pence and Democratic challenger Kamala Harris and limit the risk of Covid transmission when they go head-to-head in a debate in Salt Lake city, Utah, on Wednesday. Both candidates have recently tested negative.
President Trump, meanwhile, returned to the White House yesterday after being hospitalised with the virus.
While at Walter Reed Medical Center, he was treated with dexamethasone - a steroid medication usually given to severe and critical Covid-19 patients - and supplemental oxygen.