BRUSSELS — Nearly a year after the State Department discovered that something terrible had happened to diplomats and their spouses posted in Havana, Secretary of State Rex W. Tillerson said Wednesday that the United States remained convinced the personnel were victims of “targeted attacks.”

Mr. Tillerson also suggested that Cuba could have stopped the attacks, which the State Department has said left 24 people, who are associated with the American Embassy in Havana, with medical problems. His remarks came after The Associated Press reported that medical tests had revealed perceptible physical changes in the brains of some of the diplomats, leading experts to become increasingly skeptical that the attackers had used a sonic weapon, which had been initially suspected because the diplomats reported strange sounds in their homes or hotels.

Sonic weapons do not cause the kind of physical changes seen in the personnel, experts have said. Instead, the sounds may have been a byproduct of something else that caused the damage, The Associated Press reported.

The United States has never accused the Cuban government of perpetrating the attacks, but officials have said that Cuba, as the host government, was responsible for ensuring the safety of its diplomats and their spouses.