The video, posted on Twitter on Saturday evening, comes after mixed messages earlier in the day about his health, after a Covid-19 diagnosis.
The president’s physician said late on Saturday that Mr Trump was doing well and had made “substantial progress since diagnosis”.
Mr Trump is spending his second night in hospital.
Dr Sean Conley said in a statement that “while not yet out of the woods, the team remains cautiously optimistic” about the president’s condition.
A few hours earlier, in the four-minute video message, Mr Trump, dressed in a suit jacket and shirt with no tie, thanked the doctors and nurses at the Walter Reed National Military Medical Center close to Washington DC, where he is being treated.
“I came here, wasn’t feeling so well, I’m much better now,” he said, later adding: “Over the next period of a few days I guess that’s the real test. We’ll be seeing what happens over those next couple of days.”