WASHINGTON—Secretary of State Rex Tillerson said the U.S. is considering closing its embassy in Cuba in response to what he has described as “health attacks” on American diplomats there that have caused hearing loss, concussions and other symptoms.

Mr. Tillerson said in a television interview Sunday on CBS that he is considering calls from Republican senators to close the embassy in Havana. It was reopened in July 2015 as part of the Obama administration’s push to normalize ties with Cuba.

“We have it under evaluation. It’s a very serious issue with respect to the harm that certain individuals have suffered,” Mr. Tillerson said. “We’ve brought some of those people home. It’s under review.”

Officials at the Cuban embassy in Washington, D.C., didn’t immediately respond to a request for comment.

The health problems began last December and have recurred as recently as August, the State Department has said. The department has confirmed that at least 21 Americans have been affected.