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4 year oldJust before a scheduled briefing from his doctors, Mr Trump tweeted he would be leaving at 18:30 (22:30 GMT), adding that he felt "really good".
But questions remain over the seriousness of Mr Trump's illness after a weekend of conflicting statements.
The true scale of the outbreak at the White House remains unclear.
"Feeling really good!" Mr Trump tweeted.
"Don't be afraid of Covid. Don't let it dominate your life. We have developed, under the Trump Administration, some really great drugs & knowledge. I feel better than I did 20 years ago!!"
There are more than 7.4 million Covid-19 cases in the US and the virus has killed nearly 210,000 Americans, according to Johns Hopkins University.
The president's discharge comes as more new cases have been reported among White House staff.
At least 12 people close to Mr Trump have now tested positive, as have several junior staff members.
Many of the people who have tested positive around President Trump attended a meeting at the White House on 26 September that is being scrutinised as a possible "super-spreader event".
The White House has not revealed how many staff members have tested positive since Mr Trump's own diagnosis.
Press secretary Kayleigh McEnany became the latest high-profile figure close to the president to confirm a positive test earlier on Monday.
US media said two other aides to the press secretary had had a positive result. Ms McEnany was seen speaking to journalists without wearing a mask on Sunday but said no members of the press had been listed as close contacts by the White House medical unit.
First Lady Melania Trump, senior aides and three Republican senators have also tested positive.
President Trump's diagnosis has upended his election campaign, as he faces Democratic challenger Joe Biden on 3 November.
First Lady Melania, who is 50, has been isolating at the White House, reportedly with mild symptoms. In a tweet she said: "I am feeling good [and] will continue to rest at home".
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