US President Donald Trump says he is doing well, but that the next few days will be the "real test".

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."

He said he wanted to get back on the campaign trail. Mr Trump faces Joe Biden in the 3 November presidential election.

The positive Covid-19 diagnosis, made public by the president in a tweet early on Friday, has upended his campaign and also cast doubt on his attempt to get a new Supreme Court judge confirmed before polling day.

On Saturday morning, Dr Conley said the president was not being given extra oxygen for now and had been fever-free for 24 hours.

The president is expected to remain at Walter Reed for a "few days", according to the White House.

Dr Conley said he was "cautiously optimistic" about Mr Trump's condition but that he could not give a timetable for his discharge.

However, the White House chief of staff, Mark Meadows, expressed concern about the president's condition, saying he was not yet on a clear path to recovery.

He told reporters the president's vital signs over the last 24 hours had been "very concerning" and that the next 48 hours would be critical.

The president, being 74, a man and someone categorised as obese, is in a higher-risk category for Covid-19. He has so far been treated with an experimental drug cocktail injection and antiviral medication remdesivir.

At Saturday's news conference, Dr Conley refused to say whether the president had ever been on oxygen despite being repeatedly questioned. "None at this moment and yesterday with the team, while we were all here, he was not on oxygen," he said.

Shortly afterwards, several US media reported that doctors had given the president supplemental oxygen at the White House on Friday before deciding to transfer him to Walter Reed. It was not clear whether he had trouble breathing and needed it.

In an evening statement, Mr Trump's medical team said the president completed a second dose of remdesivir.

They said he spent most of the afternoon "conducting business and moving about the medical suite without difficulty".

First Lady Melania Trump, who also tested positive for Covid-19, is said to be doing well, and continues to rest at the White House.

Dr Conley did not respond to questions about when and where he believed Mr Trump had been infected. A crowded Rose Garden event last weekend, when the president formally announced his nomination of the conservative Amy Coney Barrett for the Supreme Court, is coming under intense focus.

Aside from the president and the first lady, six other people who attended are now confirmed to have the virus. On Saturday, campaign adviser and former New Jersey Governor Chris Christie became the latest to report a positive result.

Other people to have tested positive around Mr Trump include close aide Hope Hicks - believed to be the first to show symptoms - campaign manager Bill Stepien and former White House counsellor Kellyanne Conway.

Meanwhile, Republican Majority Leader Mitch McConnell said the Senate would postpone its work in full session until 19 October, but that work at the Judiciary Committee - which will examine Judge Barrett's nomination - would continue.

Later on Saturday, the senator said in a tweet he had had a phone call with the president, who sounded "well and says he's feeling good".

Mr Trump remains in charge. Vice-President Mike Pence, to whom under the constitution the president would transfer power temporarily should he become too ill to carry out his duties, tested negative.

The president was last seen in public on Friday evening. Before being flown to the military hospital he waved and gave a thumbs-up to reporters but said nothing before boarding his helicopter.

"I think I'll be back soon and I look forward to finishing up the campaign the way it was started," Mr Trump said in his Twitter message.

The president's campaign team said on Saturday it will move forward "at full speed" until Mr Trump can return to the campaign trail.

It is calling on top "surrogates", including Mr Trump's sons Donald Jr and Eric, and Vice-President Mike Pence to "carry the campaign forward" for the time being.

Dubbed "Operation Maga", a campaign spokesperson told Fox News the first event will be a virtual rally on Monday.

Vice-President Pence, who tested negative on Friday, is scheduled to debate Democratic vice-presidential nominee Kamala Harris on Wednesday.

Democratic challenger Joe Biden has continued his campaign and held a virtual event on Saturday. (Text, excluding headline, courtesy BBC)

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