Dr Sean Conley said in a statement the president's vital signs and physical exam remain stable.
"Overall he continues to do extremely well," Dr Conley said.
He added that Mr Trump's oxygen saturation level - an indicator in treating the disease - is at 95% to 97%, within the normal range.
The illness has also affected senior military officials.
On Tuesday, the Pentagon said top US military leaders are self-isolating after a senior Coast Guard official tested positive for the coronavirus.
The chairman of the Joint Chiefs of Staff, Gen Mark Milley, was among those affected.
There are at least 16 cases among White House staff and recent visitors to the complex so far, including press secretary Kayleigh McEnany and Hope Hicks, a counsellor to the president.
But Dr Jesse Schonau, a White House physician, says Vice President Mike Pence's daily tests have all come back negative.
His Democratic presidential challenger, Joe Biden tested negative for COVID-19 on Tuesday, his campaign said in a statement.
Mr Trump, who tweeted that he was "feeling really good" on Monday, spent three nights in hospital at the Walter Reed Medical Center.
But the president - who is still infectious - appeared to be breathless upon his return to the White House.
Mr Trump's positive update on his own wellbeing may not be a good sign, a medical expert has warned.
Dr David Strain, senior clinical lecturer at the University of Exeter, said it was "likely to be a side effect of the high-dose dexamethasone".
He explained that high-dose corticosteroids "are well established to generate euphoria and insomnia", adding: "Paradoxically, however, they may also be associated with psychiatric reactions including profound mood swings, irritability and behavioural disturbance."
Dr Strain explained that Mr Trump's doctors will be "carefully observing not only his physical health but also his mental wellbeing" while he is on this medication - and as he "comes down" afterwards.
Shortly after his return, the US president released two videos, telling Americans to "get out there" and "don't be afraid" of COVID-19 - despite the more than 210,000 coronavirus-related deaths recorded so far in the US.
"We're going back to work, we're going to be out front... I know there is a risk, there is a danger, but that's okay," he said.
And, with less than a month until the election on 3 November, he added that he was "looking forward" to the next presidential debate against Mr Biden on 15 October in Miami.
Ms McEnany said on Tuesday the rise in COVID-19 cases at the White House is not disrupting the functioning of the administration, even as US media reported two more members of the administration have tested positive for the disease.
One of Mr Trump's valets, an active member of the US military who travelled with the president last week, is one of them, Bloomberg News said on Twitter, quoting anonymous sources.
NBC, Bloomberg and CNN also reported that a military aide to the president has COVID-19.