WASHINGTON—Mosquitoes carrying the dangerous Zika virus are expected to begin infecting Americans within the U.S. in the next “month or so,” the government’s top infectious disease expert said Sunday, as officials race to prevent a widespread outbreak of the virus that is believed linked to birth defects.

Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said on ABC that more than 500 Americans already have the Zika virus. But he said all those cases are travel-related, meaning the individuals...