Sean Conley said the president also had "detectable levels of Covid antibodies" and had not needed any supplemental oxygen since he was taken to hospital.
Mr Trump, who went to hospital on Friday and was discharged on Monday, said: "I feel great!"
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 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 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 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.
What is in the latest health report?
The report from Dr Conley said: "His physical exam and vital signs, including oxygen saturation and respiratory rate, all remain stable and in normal range."
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