MEXICO CITY—The man in charge of Mexico’s response to the coronavirus pandemic says he isn’t convinced that the virus is any more lethal than an ordinary influenza outbreak, but he still worries about its capacity to overwhelm the country’s hospital system given the speed of its transmission.

“I don’t know yet. The WHO says it could be 10 times that of influenza, but I think we need to see more evidence,” Mexico’s deputy health minister, Hugo López-Gatell, said in an interview with The Wall Street Journal, referring to how...