Sean Conley also said the president had not needed any supplemental oxygen since going to 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 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.

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."

It added: "The president's labs demonstrated detectable levels of SARS-CoV-2-IgG antibodies on Monday October 5th."

Levels drawn last Thursday had shown "undetectable" antibodies.

"We'll continue to closely monitor and I will update you as I know more," the doctor said.

The body makes antibodies to help fight the infection, and coronavirus antibodies in the blood indicate a person has had the virus. However, it remains unknown whether their presence will prevent the person getting the virus again.

Mr Trump returned to the Oval Office on Wednesday afternoon to be briefed on Hurricane Delta in the Gulf of Mexico and the latest on talks with Democrats about a stimulus package for the economy, officials said.

Mr Trump has been in a defiant mood since returning from hospital, angling to work in the Oval Office rather than in the Residence, as well as pushing for an address to the nation and a resumption of campaign activity.

But many of his aides and staff remain in self-isolation.

Earlier in the day, chief of staff Mark Meadows said that anyone interacting with Mr Trump had been wearing "full PPE, masks, goggles and the like".

A memo on Monday called for limited traffic on the first floor of the West Wing and at the Residence, with strict measures on protection equipment and hand sanitiser for anyone within six feet (two metres) of the president.

Reports said there did appear to be much more mask-wearing at the White House, which had been criticised by many opponents for its lax attitude before Mr Trump's infection.

Although the names of many people who have interacted with the president and tested positive are now known, it remains unclear just how many were exposed at the White House. At least nine White House employees have tested positive but the cluster could be much higher.

Some staff have expressed concern to US media that they were exposed without their knowledge to people who were known to be infected or were at risk of being Covid-positive.

Leading Democrat Nancy Pelosi said the White House was "one of the most dangerous places in the country", adding she would "not go anywhere near it".

Stephen Miller was the latest aide to test positive - on Tuesday. Press Secretary Kayleigh McEnany and at least three other press staff have also been infected.

Several senior military leaders are also quarantining after Coast Guard official Admiral Charles Ray tested positive.

Opinion polls over the past week have suggested Mr Biden had a lead of between eight and 12 percentage points over Mr Trump nationwide, but it is likely the election will be decided in battleground states where the race is often closer.

On Tuesday, Mr Trump said he was ending negotiations with the Democrats over a Covid-19 relief bill and would only resume talks after the election.

After a negative stock market reaction, Mr Trump said he would support some stand-alone bills, later tweeting: "Move fast, I am waiting to sign!" a bill for $1,200 (£930) stimulus cheques to the American people.

Mr Meadows said there were about "10 things that we can do on a piecemeal basis".

Ms Pelosi said Mr Trump was "rebounding from a terrible mistake".

She reportedly was in talks with Treasury Secretary Steven Mnuchin on Wednesday on the possibility of a bill to aid US airlines.

It is usually seen as a bit of a sideshow, but this time the TV debate between Kamala Harris and Mike Pence promises to be like no other.

Ms Harris, a tough interrogator, is attempting to become the first female vice-president in history.

Mr Pence is just as tough in debating and rarely puts a foot wrong.

But many will be thinking about the two presidents - the two oldest candidates in history - and who would be best suited to step up if necessary.

Plexiglass will be used to separate Mr Pence and Ms Harris when they debate in Salt Lake City, Utah. Both candidates tested negative for Covid on Tuesday.

Voters will also hope for some policy discussion after the nasty and disruptive food fight between Mr Trump and Mr Biden.

The next one of those is set for 15 October, although just what form it takes, if any, remains to be seen.

Mr Trump has vowed to be there. Mr Biden says his opponent would have to be no health concern and he will take medical advice on whether to attend.