The White House released photos of the US president on Saturday night, appearing hard at work in his suite at the Walter Reed National Military Medical Centre.
After a "very concerning" period on Friday, Mr Trump could be discharged from hospital on Monday as his condition continues to improve, doctors said on Sunday.
Sharing the photos of him at the hospital, the president's daughter, Ivanka Trump, said on Twitter: "Nothing can stop him from working for the American people. RELENTLESS!"
But eagled-eyed commentators have accused Mr Trump of staging the photos.
White House reporter Andrew Feinberg took a closer look at the photos and found that Mr Trump "appears to be signing his name to a blank sheet of paper".
Watch: Trump arrives at White House, removes mask immediately
"The White House has released these photos which purport to show @realDonaldTrump 'at work' at Walter Reed National Military Medical Centre," he wrote on Twitter.
"ZOOM: @realDonaldTrump appears to be signing his name to a blank sheet of paper in this photo."
Meanwhile, Jon Ostrower, editor-in-chief of The Air Current, looked at the data from the photos, and revealed they were taken 10 minutes apart but showed Mr Trump working in two different places.
The photos released by the WH tonight of the president working at Walter Reed were taken 10 minutes apart at 5:25:59 pm and 5:35:40 pm ET Saturday, according to the EXIF data embedded in both @AP wire postings that were shared by the White House this evening. pic.twitter.com/EzeqIkGdf7
— Jon Ostrower (@jonostrower)
"The photos released by the WH tonight of the president working at Walter Reed were taken 10 minutes apart at 5:25:39 pm and 5:35:40 pm ET Saturday, according to the EXIF data embedded in both AP wire postings that were shared by the White House this evening,” he said on Twitter.
Historian Alex von Tunzelmann added: “Not a huge surprise that these photos are staged - and I’m amused by those pointing out that if you zoom in he’s just signing a blank sheet of paper - but it’s genuinely appalling that he still won’t wear a mask.
"I hope his vanity hasn’t caused the photographer to be infected.”
— Andrew Feinberg (@AndrewFeinberg)
Others on social media branded the president a "reality TV star".
"As far as he’s concerned, he just had to shoot a couple of promos for the ‘look presidential’ bit he performs," they said.
Another wrote: "That’s the only kind of ‘work’ he knows how to do.
Not a huge surprise that these photos are staged - and I’m amused by those pointing out that if you zoom in he’s just signing a blank sheet of paper - but it’s genuinely appalling that he still won’t wear a mask. I hope his vanity hasn’t caused the photographer to be infected. https://t.co/NymuomAuUZ
— Alex von Tunzelmann (@alexvtunzelmann)
"And in his mind, as long as he makes it look like he’s working and his base believes it, that’s every bit as good, if not better, than actually doing something."
Speaking outside the hospital on Sunday, the president's medical team said his condition had "continued to improve".
Dr Brian Garibaldi, a specialist in pulmonary critical care, said Mr Trump received a second dose of remdesivir on Saturday, along with a dose of dexamethasone following a drop in oxygen levels.
Dr Garibaldi said Mr Trump was given dexamethasone in response to "transient low oxygen levels".
"He received his first dose of that yesterday and our plan is to continue that for the time being," he said.
Dr Conley confirmed the president had a "high fever" and a blood oxygen level below 94 per cent on Friday.
Dr Conley said the president's oxygen level had also dropped to 93 per cent on Saturday, but he was not experiencing breathing difficulties.
His oxygen level currently stands at 98 per cent, the president's medical team said.
Mr Trump released a four-minute video on Saturday in which he said the "real test" of his condition will come over the next few days.
"Over the next period of a few days, I guess that's the real test, so we'll be seeing what happens over those next couple of days," Mr Trump said into the camera, looking tired and wearing a jacket and open-necked shirt.
On Saturday, Mr Meadows told reporters outside the hospital: "We're still not on a clear path yet to a full recovery."
Mr Trump's chief doctor had also expressed cautious optimism, but added that the president was "not yet out of the woods".
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