Mehra said in a statement these drugs should not be used as treatments for COVID-19 outside of clinical trials.
The drugs should only be used for COVID treatment as part of robust studies that will definitively show their impact, the researchers said.
It comes just days after the United States president's decision to take hydroxychloroquine was described as "a staggering, irresponsible act that could very well also amount to self-harm" and there are fears his actions risk running down supplies of the drug for people with other conditions who need it.
And neither drug benefitted patients hospitalised with COVID-19, according to a study published on Friday in The Lancet. The evidence for the drug's effectiveness, however, hasn't been established, although ongoing rigorous trials randomly assigning patients to receive hydroxychloroquine or placebo are still ongoing (including one headed by the U.S. National Institutes of Health).
"Several countries have advocated use of chloroquine and hydroxychloroquine, either alone or in combination, as potential treatments for COVID-19", said Frank Ruschitzka, director of the Heart Center at University Hospital Zurich and co-author of the study.
Professor Stephen Evans, from the London School of Hygiene and Tropical Medicine, said more research was needed, but added: "it is clear that the drugs should not be given for treatment of Covid-19 other than in the context of a randomised trial".
A study published Friday in a prestigious medical journal found that the anti-malarial drug President Donald Trump claims he is now taking-and has repeatedly urged others to take-is not effective for treating Covid-19 and could increase risk of heart problems and death in coronavirus patients.
Trump said Wednesday that he will finish taking hydroxychloroquine this week, and has not reported any health issues.
The World Health Organization (WHO) has previously warned against self-medicating with hydroxychloroquine, with the study in the United Kingdom involving front line health workers, carried out in a controlled environment.
The UK Government has said that chloroquine and hydroxychloroquine are not licensed to treat Covid-19 related symptoms or prevent infection.
They explained chloroquine, an antimalarial drug and its analogue, hydroxychloroquine, are commonly used to treat autoimmune diseases including lupus and arthritis.
Researchers estimate that the death rate attributable to use of the drugs, with or without an antibiotic such as azithromycin, is roughly 13% versus 9% for patients not taking them.
Those who were treated with hydroxychloroquine had a mortality rate of 18 percent. However, he said that due to the enthusiasm some Americans have for the drug and the Lancet study's findings, randomized trials are even more important.
More than 96,000 people, all of whom had been hospitalized with COVID-19, were included in the study.
The difficulty with observational (sometimes called "real-world") studies is that, often, the patients whom doctors choose to treat with a drug are different - in this case, probably sicker - than those who go untreated.
The team also found that serious cardiac arrhythmias, which cause the lower chamber of the heart to beat rapidly and irregularly, were more common in all the groups receiving one of the four treatment regimens.
The drugs were thrust into the spotlight by Trump, who said he requested hydroxychloroquine from his physician, Dr. Sean Conley.