Trump is under federal investigation for possible violations of the Espionage Act
But Trump demonstrated no such restraint at a White House press briefing on Monday.
"The hydroxychloroquine and the Z-Pak, I think as a combination probably is looking very, very good," he said.
"There's a real chance that it could have a tremendous impact, it would be a gift from God, if that worked it would be a big game changer," he added, quoting the example of a patient who was ill but recovered after taking the drug.
NBC reported that a woman in Arizona, who heard Trump talk about chloroquine, ended up in hospital and her husband died after they took a form of chloroquine she had used to treat her koi fish.
"I saw it sitting on the back shelf and thought, 'Hey, isn't that the stuff they're talking about on TV?'" NBC quoted the unnamed woman as saying.
Banner Health, a non-profit health care provider based in Phoenix, said on its website that "a man has died and his wife is under critical care after the couple, both in their 60s, ingested chloroquine phosphate, an additive commonly used at aquariums to clean fish tanks."
Banner Health warned against self-medicating to treat or prevent the Covid -19 illness.
Trump has been criticized by some in the scientific community for overhyping the drugs - which could create shortages for Americans who need them to treat lupus and rheumatoid arthritis, diseases for which they are approved.
New York is set to begin a clinical trial on Tuesday that would treat patients with hydroxychloroquine taken together with azithromycin, an antibiotic used to clear secondary bacterial infections.
Separately, Vice President Mike Pence announced that self-administered nasal swab tests for the illness would be made available this week, thus reducing part of the burden on the overstretched health care system.
At present, the test is administered by health care workers wearing personal protective gear which is in short supply.
The US has almost 44,000 cases and 560 deaths, according to a tracker maintained by Johns Hopkins University.
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This was done to 'move to a point where the virus no longer severely disrupts our daily lives'