Dr Sean Conley said the president had responded "extremely well" to medication and had "remained stable".
Mr Trump later said he would probably take another Covid test on Friday and hoped to hold a rally over the weekend.
The president earlier pulled out of next Thursday's TV debate with Democratic rival Joe Biden.
He said he was "not going to waste my time on a virtual debate" after organisers said it would have to take place remotely because Mr Trump had tested positive for coronavirus.
The move sparked a row about how and when further debates would take place.