The news came hours after the president disclosed over Twitter that he and first lady Melania Trump had tested positive.
Trump is “in good spirits,” and spoke Friday morning to White House chief of staff Mark Meadows, according to NBC News.
The White House is discussing whether the president will address the country in some manner about his diagnosis.
Trump, who is 74 years old and overweight, is in categories of people considered at high risk for adverse effects from the disease.
Vice President Mike Pence and his wife both tested negative for the virus, the White House announced later Friday. Pence is next in line for the presidency.
White House physician Dr. Sean Conley said in a memo early Friday that he expects Trump to “continue carrying out his duties without disruption while recovering.”
A White House official told CNBC that some staffers who were in contact with the president on Thursday are working from home on Friday.
Trump said in his early morning tweet Friday that he and his wife were beginning their quarantine process after the positive test. Centers for Disease Control and Prevention guidelines recommend people who believe they may have been exposed to the virus should quarantine for 14 days.
Trump debated Democratic presidential nominee and former Vice President Joe Biden on Tuesday and is scheduled to appear in the second debate on Oct. 15, 13 days after he disclosed his diagnosis. The Commission on Presidential Debates didn’t immediately respond to a request for comment on how Trump’s diagnosis would impact the debates.
The White House physician’s memo came hours after Trump said he would begin the quarantine process after top aide Hope Hicks tested positive for the virus. Hicks had traveled with the president to Tuesday’s debate in Cleveland and was seen not wearing a mask.
Trump’s handling of the coronavirus has been a top issue in the run-up to the 2020 election. In the United States, more than 7.2 million have been infected and more than 207,000 people have died, according to a tally from Johns Hopkins University.
In a taped interview with journalist Bob Woodward, Trump said in mid-March he intentionally played down the virus in order not to “create a panic,” according to CNN, which published audio of the interview. Trump has pushed for schools, businesses and sports leagues to reopen even as cases of the virus rise and has held campaign events where attendees pack closely together, many without masks.
The Trump administration’s messaging about masks has been inconsistent throughout the pandemic. Officials initially guided Americans not to wear them so they could be reserved for medical professionals, but health officials now advise most people to wear some form of face covering to prevent the spread of the virus.
Still, at Tuesday’s debate, Trump bashed Biden for wearing masks in many of his public appearances.
“I don’t wear masks like him. Every time you see him, he’s got a mask. He could be speaking 200 feet away and he shows up with the biggest mask I’ve ever seen,” Trump said at the event.
— CNBC’s Eamon Javers contributed to this report.