Sean Conley also said the president had not needed any supplemental oxygen since going to the hospital on Friday. He was discharged on Monday.
Mr. Trump said he “felt great!” and later returned to the Oval Office for briefings, the White House said.
The news comes ahead of the key vice-presidential TV debate later.
Wednesday’s debate between Mike Pence and Kamala Harris is one of the most eagerly anticipated in years.
Many observers branded the first presidential TV debate between Donald Trump and Democratic challenger Joe Biden as “ugly” and “chaotic”. Very little on the policy was aired as the debate, on 29 September, descended into interruptions and insults.
Mr. Trump’s supporters say that he has shown leadership since his release from the hospital on Monday. His opponents say his behaviour has become increasingly erratic.
The White House has also set out new safety measures after President Trump’s return from the hospital and the news that another aide had Covid-19.
The presidential election is on 3 November. One key issue in the run-up is a coronavirus stimulus package for the economy. Mr. Trump appeared to abandon negotiations with the Democrats on Tuesday, only to say later he would agree to some measures individually.