"The White House medical team and I will maintain a vigilant watch, and I appreciate the support provided by some of our country's greatest medical professionals and institutions.
"Rest assured I expect the President to continue carrying out his duties without disruption while recovering, and I will keep you updated on any future developments."
Dr Conley, who became the president's physician in May 2018, is a US Navy veteran and is qualified in osteopathic medicine.
Following a physical examination in February 2019, Conley said the president was in "very good health" and should remain so "for the remainder of his presidency and beyond".
Trump turned 74 in June.
The US Centres for Disease Control and Prevention states older adults are at highest risk of Covid-19.
Eight out of 10 Covid-19 deaths reported in the US have been in adults aged 65 and above.
The first presidential debate was held on Tuesday between Trump and Democratic challenger Joe Biden in Cleveland, Ohio.
The president travelled on Air Force One to and from the debate with political adviser Hope Hicks who contracted the infectious disease, prompting the Trumps to get tested.
