Dr Sean Conley made the comments as he gave an update on Mr Trump’s condition as he is being treated at the Walter Reed National Military Medical Centre near Washington DC. He said the president was “doing well” and only suffering mild symptoms on Thursday night.
But by late Friday morning Mr Trump had a high temperature and his oxygen levels were dipping, Dr Conley said.
He added that he was “concerned for possible rapid progression of the illness”.
Mr Trump was moved to hospital later that day.
In his update today, Dr Conley said Mr Trump’s condition is improving and he could return to the White House as early as Monday.
He said: “The patient continues to improve.
“He has remained without fever since Friday morning, his vital signs are stable.”
Mr Trump, who tested positive for coronavirus on Thursday evening, took to social media on Saturday to post a four-minute video declaring he felt “much better”.
He said: “I came here, wasn’t feeling so well, I feel much better now.
He said the president is being given the “best” medical care available.
Mr Johnson told the BBC’s Andrew Marr Show: “I’m sure that President Trump is going to be fine, he has got the best possible care.
“The most important thing to do is follow his doctors’ advice.”
Brexit Party leader Nigel Farage, an ally of Mr Trump’s, said he thought the president looked “pretty robust”.
Speaking to Sky News’ Sophy Ridge On Sunday, he said: “He has got Covid-19, he has been ill, he’s been put into hospital, he’s been put on oxygen.
“But considering all of that, he looked pretty robust.”
Mr Farage said it remains to be seen whether the president’s case of the virus will “bite hard or not”
He added: “He doesn’t drink, he doesn’t smoke, he’s carrying a few extra pounds but he is generally in pretty robust health, so my guess would be he is going to be OK.”