The 79-year-old, who is fully vaccinated and has twice obtained booster shots, is suffering "very mild symptoms" and will keep doing all his duties, press secretary Karine Jean-Pierre said. The President is taking the antiviral medicine Paxlovid, her statement added.
In a tweet Mr. Biden said he was "doing great" and "keeping busy". His wife First Lady Jill Biden said she had tested negative.
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Consistent with White House protocol, the President will continue to work in isolation until he tests negative, Ms. Jean-Pierre said - and will participate in meetings via telephone and Zoom.
White House Covid coordinator Dr. Ashish Jha said the President was exhausted, with a runny nose and dry cough.
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He said Mr. Biden went to bed feeling fine but did not sleep well and tested positive on Thursday morning.
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In a press briefing at the White House on Thursday afternoon, Ms Jean Pierre said that Mr. Biden had kept working throughout the day and held calls with a number of US mayors and government officials.
Dr. Jha said that Mr. Biden's vaccination condition meant that his risk of serious illness was "dramatically lower", and was further reduced by the antiviral drug he was now taking. He added that Mr Biden will return to normal activities after a negative test.
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The White House medical unit will inform all close contacts of the President during the day, Ms. Jean-Pierre said earlier, including any members of Congress or press members who were with Mr. Biden during his visit to Massachusetts on Wednesday. It is unclear where he was infected.
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First Lady Mrs Biden said she had spoken to her husband and he was "doing fine".
"He's feeling good. I tested negative this morning. I'm going to keep my schedule. According to CDC guidelines, I'm keeping masked," she said.
Mr. Biden, who is the oldest President in US history and turns 80 this year, last tested negative for Covid on Tuesday, the White House said.
Mr. Biden was judged "fit for duty" and described as "healthy" and "vigorous" by his physician, Dr Kevin O'Connor, during his last physical examination in November, according to the BBC's US partner CBS.
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As the pandemic has spread, doctors have come to realize more about who is at most significant risk of getting seriously ill if they catch Covid and what care they might need.
Age is a big factor - generally, the older you are the higher the risk - as well as how fit and healthy you were beforehand.
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