At least one outside expert said the approach could present safety risks. Paul Knoepfler, a stem cell researcher at the University of California, Davis, said that patients with coronavirus can develop severe reactions where their immune systems go too far in attacking cells in their lungs, causing damaging inflammation. Other cell therapies tested in China are designed to dampen the immune response. He said one risk with the natural killer cells is they could go in the other direction, exacerbating respiratory problems “by massive killing of the patients’ respiratory cells.”
Despite the scant evidence, Mr. Giuliani has become an early booster, interviewing Dr. Hariri on a podcast published on his website Saturday, and praising the treatment on Twitter, saying, “this therapy has real potential.” In a tweet on Saturday, he added, “Let’s hope F.D.A. can recognize that their cumbersome process designed to keep us safer, if it is not altered dramatically in times of great need, can result in unimaginable loss of human life.”
Around the same time, Twitter deleted a post by Mr. Giuliani that it said violated its rules. The tweet, from March 27, made unfounded claims about the malaria drug hydroxychloroquine, one of the treatments that Mr. Trump has supported.
Dr. Hariri said that he has known Mr. Giuliani for years and that the appearance on his podcast was “a friendly chat between people who know each other and who share a common interest in this particular response to this disease.”
He said that he has no business relationship with Mr. Giuliani, and that Mr. Giuliani is not representing him in any way, either paid or unpaid. “I don’t have anything to do with what the mayor tweets or whatnot, and I don’t agree or disagree with anything,” he said.
Dr. Hariri said the company would follow the established process for testing whether a drug works. “We have waited for the F.D.A. to complete their review, which they did in a heroic and quick fashion,” he said.
On Wednesday evening — the same day the F.D.A. approved his trial — Dr. Hariri praised the appearance by the agency’s commissioner, Dr. Stephen Hahn, on the conservative Fox News talk show “The Ingraham Angle.”
“We are fortunate to have Dr. Hahn at the helm,” he tweeted.