Dr Sean Conley said in a memo released by the White House that Mr Trump had responded “extremely well” to treatment without any evidence of adverse effects.
The US leader was hospitalised on Friday after he announced he had contracted Covid-19. He returned to the White House on Monday.
“Since returning home, his physical exam has remained stable and devoid of any indications to suggest progression of illness,” Conley wrote.
“Based on the trajectory of advanced diagnostics the team has been conducting, I fully anticipate the President’s safe return to public engagements at that time.”
Mr Trump, confined to the White House with the illness, has been itching to return to the campaign trail as he trails his rival in polls ahead of the November 3 election.
The president has been criticised both for his administration’s handling of the pandemic and for his response to his own diagnosis.
Earlier on Thursday Mr Trump said did not believe he was contagious and was feeling good enough to resume campaign rallies.
Mr Trump has held such rallies indoors and outdoors with thousands of people, many of whom do not wear masks, against the advice of public health professionals.
“I’d love to do a rally tonight. I wanted to do one last night,” Mr Trump told Fox Business Network, adding that “if I’m at a rally, I stand by myself very far away from everybody.”
The White House has declined to say when Mr Trump last tested negative test for the virus.
The president’s positive test sidelined him from in-person events that have been the lifeblood of his campaign.
Mr Trump pulled out of a second debate with Democratic hopeful Joe Biden after the Commission on Presidential Debates announced that the October 15 event would be held in a virtual format.
The move was made to ensure it could go forward whether or not Mr Trump remained virus-free.
“I’m feeling good, really good,” Mr Trump said in the Fox interview.
The president said he had stopped taking “most therapeutics” for the virus but was still on steroids.