Joe Biden has said he and Donald Trump "shouldn't have a debate" as long as the president remains positive for coronavirus.
The Democratic presidential candidate said he was "looking forward to being able to debate him" but that "we're going to have to follow very strict guidelines”.
It comes the Republican president tweeted to say he was "feeling great" and looking forward to next week's face-to-face Mr Biden despite doctors saying he is still contagious with Covid-19.
The US president was diagnosed with the virus last week and was taken to Walter Reed National Military Medical Centre where he stayed for three nights.
He staged a return to the White House on Monday.
Mr Biden told reporters while boarding his plane back to Delaware in Hagerstown, Maryland, on Tuesday: "I think if he still has Covid, then we shouldn't have a debate."
The next debate is scheduled for October 15, with a third debate due to take place on October 22.
Mr Biden's campaign says he tested negative for Covid-19 earlier on Tuesday.
The president ignited a new controversy by declaring that, despite his illness, the nation should not fear the virus that has killed more than 210,000 Americans.
Landing at the White House on Marine One, Mr Trump gingerly climbed the South Portico steps, removed his mask and declared: “I feel good.”
Mr Biden criticised Mr Trump for downplaying the severity of coronavirus, saying there is "a lot to be concerned about".
He also said the president should be communicating the "right lesson" on masks and social distancing.
Mr Trump’s doctor Navy Commander Sean Conley said earlier that the president remained contagious and would not be fully “out of the woods” for another week.
The president is expected to continue his recovery at the White House, where the reach of the outbreak that has infected the highest levels of the US government is still being uncovered.
