Medical experts are questioning Donald Trump's decision to greet supporters in a drive-past outside the hospital where he is being treated for Covid-19.
There are concerns the US president, who wore a mask, may have endangered Secret Service staff inside the car.
White House spokesperson Judd Deere said the trip on Sunday had been "cleared by the medical team as safe".
Questions remain over the seriousness of Mr Trump's illness after conflicting statements over the weekend.
The doctors treating the president in hospital are expected to provide an update on his condition at 15:00 local time (19:00 GMT).
Speaking on Fox News, White House chief of staff Mark Meadows said doctors would decide later whether the president could be discharged from Walter Reed hospital, near Washington, on Monday.
Mr Meadows said he had spoken with Mr Trump earlier, and that his condition appeared to have improved overnight. The president was taken to hospital on Friday evening, hours after announcing he had tested positive for the virus.
President Trump's diagnosis has upended his election campaign, as he faces Democratic challenger Joe Biden on 3 November.
A growing number of people around the president, including his wife Melania, senior aides and Republican senators, have tested positive with the virus. Kayleigh McEnany, the White House press secretary, became the latest to report a positive result on Monday.
Covid-19 has infected nearly 7.4 million and killed nearly 210,000 people across the US, according to Johns Hopkins University.
What did the president do?
Mr Trump waved to well-wishers from behind the glass of a sealed car after tweeting that he would pay a "surprise visit" to "patriots" outside the hospital. Inside the car, at least two people could be seen wearing protective gear in the front seats, with Mr Trump sat in the back.
Experts say the president's short car trip broke public health advice to quarantine when seeking treatment for the virus, and may have put Secret Service agents inside the vehicle at risk of infection.
"That Presidential SUV is not only bulletproof, but hermetically sealed against chemical attack. The risk of Covid-19 transmission inside is as high as it gets outside of medical procedures," tweeted Dr James Philips, a doctor at the same hospital where the president is being treated.
Those inside the president's car would now need to quarantine for 14 days, he said.
Democrats have also criticised the trip, with House of Representatives Hakeem Jeffries tweeting: "We need leadership. Not photo ops."
But the White House's Judd Deere defended the move, saying "appropriate precautions were taken in the execution of this movement to protect the president and all those supporting it, including PPE [personal protective equipment]".
What did we learn at the weekend?
It emerged the president's condition was more serious than previously reported when he went to hospital on Friday evening.
The White House had said Mr Trump was experiencing "mild symptoms" of Covid-19, but then it was confirmed that he had received extra oxygen after his levels dipped twice in two days.
He was also given the steroid dexamethasone, which is normally reserved for serious cases, according to experts.
On Sunday, White House Physician Dr Sean Conley addressed widespread confusion over the state of Mr Trump's health, after conflicting accounts from him and Mr Meadows.
Dr Conley had offered an upbeat prognosis on Saturday, which was later contradicted by Mr Meadows who said the president's vital signs the previous 24 hours had been "very concerning".
"I was trying to reflect an upbeat attitude of the team and the president about the course his illness has had," Dr Conley told reporters on Sunday. "I didn't want to give any information that might steer the course of illness in another direction."
There is scepticism over the prospect - raised by doctors earlier - that Donald Trump could leave hospital as early as Monday.
The crucial questions
It has been three days since the shocking revelation that Donald and Melania Trump tested positive for the coronavirus.
As it now stands, there are a number of important questions that remain unanswered.
When did Trump last receive a negative test? Do we know all the facts about his health? Should Vice-President Mike Pence be isolating? Why has the White House been so slow to contact-trace?
How these questions are resolved could hold the key to understanding how much damage the virus will do to this president - to his health, his reputation and his political standing.
The president, being 74, a man and someone categorised as obese, is in a higher-risk category for Covid-19. On Friday he was given an experimental drug cocktail injection and started a five-day course of the antiviral medication remdesivir.
However, Mr Trump sought to project an image of strength, tweeting images of himself appearing to work from the hospital and a video message teasing his surprise drive-past on Sunday.
What do the drugs say about Trump's condition?
How significant is it that Donald Trump has been given dexamethasone? The steroid saves lives by calming the immune system, which can become dangerously overactive in Covid, but needs to be used at the right time. Give it too early and the drug could make things worse by impairing the body's ability to fight off the virus.
This is not a drug you would usually give in the "mild" stage of the disease. The Recovery Trial, which took place in the UK, showed the benefit kicked in at the point people need oxygen - which Mr Trump briefly did. The World Health Organization translated those findings to advise using the steroid in "severe and critical" cases.
Mr Trump's blood oxygen levels did dip below 94%, which is one of the National Institutes of Health criteria for "severe illness". However, those low oxygen levels were not sustained and the gap between someone needing transient oxygen support and end-stage Covid-19 is massive.
We do not know the full details of Mr Trump's condition, but it is hard to imagine you or I would be discharged from hospital while taking dexamethasone and remdesivir and after being given an experimental antibody therapy. However, we do not have the medical support at the US president's disposal.
How is Melania Trump doing?
The first lady, who is 50, has been isolating at the White House since Friday, when she described having "mild symptoms". In a tweet on Monday she said: "I am feeling good [and] will continue to rest at home".
US media reported that she would not visit the president at the hospital as that would expose her staff as well as medical workers.
Many of the people who have tested positive around Mr Trump attended a meeting at the White House on 26 September that is being scrutinised as a possible "super-spreader event".
What about the political situation?
The president's campaign team said on Saturday it would move forward "at full speed" until Mr Trump could 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.
No White House events are scheduled for Monday.
Meanwhile, Mr Pence is due to debate Democratic vice-presidential nominee Kamala Harris on Wednesday. Mr Pence and his wife Karen both tested negative on Monday morning.
Joe Biden, who has continued his campaign, is due to appear in Miami, Florida on Monday - despite having shared a stage with Mr Trump in a debate last Tuesday, when the president may have already contracted the virus. Mr Biden's campaign said he had tested negative for the virus on Sunday evening.
Republican Mike Pence and Democrat Kamala Harris will take the stage on Wednesday for the lone debate between the two vice-presidential candidates.
In a race where both presidential nominees are over 70, people have been paying particular attention to their running mates. We want to know: What questions do you have about the vice-presidential debate?
Submit your questions below.
If you can't see the form, you may need to view the site on a desktop.