The New York Greater Hospital Association and New York Democratic Gov. Andrew Cuomo have since pushed back on Trump's claims.
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Trump first made the claims on Sunday from the White House Rose Garden, where he held a press conference with his coronavirus task force. The president told reporters they should "look into it."
He repeated it at Monday's briefing after a reporter questioned him about it.
Trump implied, without evidence, that there was a nefarious reason for the shortage in masks, which states have criticized the federal government for not providing. Meanwhile, nurses and doctors across the country have resorted to re-using protective equipment, accepting donations, buying their own PPE (personal protective equipment) and other workarounds to keep themselves safe.
"How do you go from 10 to 20 to 300,000? 10 to 20,000 masks to 300,000? Even though this is different, something's going on. And you ought to look into it as reporters," Trump said. "Where are the masks going? Are they going out the back door? How do you go from 10,000 to 300,000 -- and we have that in a lot of different places," he said, though he didn't mention any other examples of hospitals that have reported stolen masks.
"I hope I didn't get any of your clients in trouble, but it could be that they are in trouble," Trump said, referring to hospitals as "clients" and speaking to the CEO of the mask-production company, who accompanied Trump at the briefing.
While there have been a handful of small-scale reports of people stealing masks, gloves and hand sanitizer from hospital waiting areas or other health centers across the country as anxieties over supply shortages rose, many quickly criticized Trump for seeming to put the blame on hospital workers.
"Of all the rotten, despicable things Donald Trump has done since taking office, blaming health care workers for the lack of masks is like top 3," Connecticut Democratic Sen. Chris Murphy wrote on Twitter.
2020 hopeful and former Vice President Joe Biden called Trump's claims "ridiculous and completely false."
“Today’s conspiracy mongering from our President is among the most reckless and ignorant moves he has made during this crisis, and there have been many. Lives hang in the balance,” Biden said in the statement Sunday.
At his daily coronavirus briefing in New York on Monday, Cuomo deflect questions about Trump's comments, saying, "I don't know what he's trying to say."
"In terms of a suggestion that the PPE equipment is not going to a correct place, I don't know what that means. I don't know what he's trying to say. If he wants to make an accusation then let him make an accusation. But I don't know what he's trying to say by inference," Cuomo said.
Asked for evidence to support Trump's comments, the White House pointed to an investigation Cuomo mentioned more than three weeks ago, at the beginning of March, when he warned that increasing anxiety was causing people to steal products and that he'd tasked the police to investigate.
"Not just people taking a couple or three, I mean just actual thefts of those products," Cuomo said on March 7. "I've asked the state police to do an investigation, look at places that are selling masks, medical equipment, protective wear, feeding the anxiety."
Asked by ABC News on Monday, the New York State Police did not provide any updates.
Kenneth E. Raske, the president of the Greater New York Hospital Association, attended the briefing on Monday with Cuomo. In a statement put out ahead of the briefing, Raske said health care workers "deserve better than their President suggesting that PPE is 'going out the back door' of New York hospitals."
"New York's healthcare workers are treating exploding numbers of COVID-19 patients around the clock – willingly and without complaint. My daughter, an ICU nurse at a New York City hospital, is one of them," Raske said. "Personal protection equipment is the single thing that separates them from being COVID-19 patients themselves. They deserve better than their President suggesting that PPE is 'going out the back door' of New York hospitals."
Dr. Anthony Fauci, the nation's top expert on infectious diseases and a key member of the White House coronavirus task force, said Monday morning that he wasn't familiar with the issue but suggested that there could be more demand because "many more" patients need them.
“You know, I have not looked at that carefully, so I can’t really can't comment. I mean, it could be that there are many more patients there that need them and they're actually not walking out the door, they're actually being utilized. I don't know. I mean, that discussion came yesterday. I really didn't know what was going on. I'd have to check that out later and find out what they were talking about," Fauci said on CNN.
The one anecdotal example the president referenced Sunday about increased mask demand at a hospital in New York City was shared with him by Ed Pesicka, the CEO of a mask production company with facilities in North Carolina, who joined Trump at the briefing Sunday. Pesicka did not, however, seem to back Trump's assumption that masks were being siphoned away from hospitals through a a "back door," as the president claimed, but rather used the anecdote as an example of the challenging uptick of demand.
Pesicka said one of the issues his company was struggling with was "the demand increase" and spoke of the hospital in New York that was requesting 200,000-300,000 masks per week, more than a ten-fold increase -- and a harbinger of demand coming down the pipeline.
"So you multiply that times the entire U.S., let alone the same demand outside of the U.S., that's part of the issue we're running into is even with a significant ramp-up in supply, you know, there's still that demand that is much greater than that supply," Pesicka said.
Pesicka did not respond to a request for comment by ABC News through his company, Owens and Minor.