Mexico's health regulator Cofepris has already twice denied approval for the drug with a "non-favorable" opinion, deputy health minister Hugo Lopez-Gatell told his regular nightly news conference.
"We have no mandate from the FDA," he said. "Cofepris has identified that the evidence does not suggest a usefulness, a sufficient efficacy."
The FDA approved remdesivir on Thursday, making it the first and only drug approved for the disease in the United States.
Remdesivir, given intravenously, was one of the drugs used to treat U.S. President Donald Trump during his bout with COVID-19.
The World Health Organization's (WHO) Solidarity drug trial last week concluded remdesivir has little or no impact on a patient's chances of surviving COVID-19, and a top WHO scientist on Friday recommended the FDA consider all available evidence.
Lopez-Gatell said Gilead had sent a letter to doctors in Mexico refuting the results of the Solidarity trial, and that officials were looking to see if the letter could be cause for sanction, given that remdesivir is not registered with Mexican health authorities.
"It confuses the population and generates a false expectation of the possibility of having a treatment option," he said.
Gilead did not immediately respond to a request for comment.
(Reporting by Sharay Angulo and Daina Beth Solomon; Editing by Sonya Hepinstall and Tom Hogue)