While there is no evidence so far that tourists or hotel employees have been affected, the government’s travel warning could cripple Cuba’s burgeoning tourism industry if tour operators, hotel and cruise line companies or their insurers decide that their employees and customers could be at risk.
“Right now, the most important constituency of determining the impact of this is not members of Congress or pundits; it’s the insurance companies,” said John Kavulich, the president of the U.S.-Cuba Trade and Economic Council. “If the carriers withdraw coverage because of this warning, then everything could shut down there almost overnight.”
The timing of Mr. Tillerson’s decision and its potential fallout promises to write yet another chapter in an extraordinary history between the two countries that has included the explosion of the American battleship Maine in Havana Harbor in 1898, the Bay of Pigs in 1961 and the Cuban Missile Crisis in 1962.
Then, in 2014, after decades of frosty relations, constant sniping and severed diplomatic relations, President Barack Obama reversed course and reached an agreement with President Raúl Castro of Cuba to reopen embassies in the countries’ respective capitals and begin to encourage nascent tourism and business ties.
But the rapprochement was deeply unpopular among a powerful segment of Cuban émigrés in Florida, and Mr. Trump in his campaign vowed to reverse what he called a “terrible and misguided deal.” Once in office, Mr. Trump did undo crucial pieces of Mr. Obama’s policy, but kept in place others that were broadly popular, such as allowing direct flights and cruises between the United States and Cuba, and rules making it easier for American companies to do business in Cuba.
On Capitol Hill, a debate began immediately over whether Mr. Tillerson acted too quickly or not quickly enough. He has known since a few days after his confirmation on Feb. 1 that diplomats in Havana were becoming ill, but took until Friday to reduce the diplomatic and Marine Corps contingent there to 27.
Senator Marco Rubio, Republican of Florida, who fiercely opposed Mr. Obama’s decision to improve ties with Cuba, questioned the decision not to punish Cuba more forcefully.
Senator Patrick J. Leahy, Democrat of Vermont, said punitive measures would only play into the hands of the attackers. “Whoever is doing this obviously is trying to disrupt the normalization process between the United States and Cuba,” Mr. Leahy said. “Someone or some government is trying to reverse that process.”
A host of Latin American scholars denounced the State Department’s travel advisory as a cynical ploy to undo the last vestiges of the Obama administration’s rapprochement with Cuba. “The fact remains that Cuba is the safest place in Latin America for foreigners to visit,” said Eric Zolov, a Cuban expert at Stony Brook University. “Crime is exceptionally low and tourism is coveted by the government.”
President Trump was unapologetic about the action on Friday, saying that “some very bad things happened in Cuba.”
But one reason Mr. Tillerson decided to keep the embassy open is a growing belief among American officials that the Cuban government was probably not responsible for them.
A former senior American official said that there was information that the Cubans were rattled by what had happened and were desperate to find the cause. The fact that a Canadian diplomat was also affected has deepened the mystery. Relations between Canada and Cuba have long been warm.
The former senior official said that F.B.I. agents who had been allowed entry to Cuba had visited the homes of the American diplomats and had not been able to detect anything. The F.B.I. has also reviewed security footage of the homes and found nothing suspicious, and the agency has been unable to duplicate the effects the diplomats have experienced in a lab.
That the Cubans offered to let the F.B.I. go to Havana and investigate was a rare level of openness and was seen as yet another indicator that the Cubans themselves have been shaken by the episode.
Of the 21 people who have become ill, 17 were government employees and four were spouses. Three of the spouses worked at the embassy. For some, the injuries appear permanent, with symptoms including hearing loss, dizziness, tinnitus, balance and visual problems, headache, fatigue, cognitive issues and difficulty sleeping. But despite an intensive investigation by the F.B.I., the cause and perpetrators of the attacks remain a mystery.
Some of those affected reported hearing odd sounds in particular rooms of their homes, leading some experts to speculate that some kind of sonic weapon or faulty surveillance device may have been at fault.
“Just looking at the symptoms, it sounds like they’ve all had traumatic brain injuries like a concussion or a series of minor head injuries even though we know they haven’t,” said Dr. Martin Gizzi, a neurologist in Portland, Ore., who is a fellow of the American Academy of Neurology.
Dr. Gizzi said neither ultrasonic nor subsonic waves have been known to produce such injuries surreptitiously. Among the other possibilities are a virus, poison or radiation, he said.
Friday’s announcement came three days after Mr. Tillerson met with Bruno Rodríguez, Cuba’s foreign minister, in Washington, in a meeting that the Cuban government requested. That meeting did not convince Mr. Tillerson that the Cubans could guarantee the safety of the remaining American employees in Havana, prompting the decision to pull much of the embassy staff.
The remaining staff will carry out only emergency services, such as helping American citizens in need. Routine visa functions for Cuban citizens will no longer be conducted in Havana. Officials may soon direct Cubans seeking to travel to the United States to apply for visas at embassies or consulates in other countries.
American officials will continue to meet with their Cuban counterparts — but not in Cuba — until the cause of the attacks is uncovered, officials said.
In August, Heather Nauert, the State Department’s spokeswoman, said that the department was confident that the attacks were no longer occurring. But on Friday, officials conceded that the remaining 27 personnel in Havana were still at risk.