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In August, the State Department said Americans linked to the U.S. embassy in the capital had experienced physical symptoms caused by such "incidents," involving sound waves, starting as far back as late 2016. Five Canadians in Havana were also affected.
In some cases the victims heard nothing, while others sensed deafening sound, but all suffered symptoms such as nausea, dizziness and temporary hearing or memory loss.
The incidents have left a sense of unease among Havana's diplomatic community, various diplomats said, and the Cuban Foreign Ministry has not provided any explanation to date.
A months-long investigation by Cuba, the United States and Canada into the mysterious affair, unprecedented in modern diplomatic history, has yet to come up with answers as to how the attacks took place, let alone who was behind them.
Cuba has denied involvement. The U.S. State Department has not blamed Havana for the attacks, but asked two Cuban diplomats to leave Washington in May. Canada does not intend to take diplomatic action "at this time," an official said in August.
In a letter, the five Republicans - Senators Tom Cotton, Richard Burr, John Cornyn, Marco Rubio and James Lankford - urged Secretary of State Rex Tillerson to remind the Cuban government of its responsibility toward diplomats.
"Furthermore, we ask that you immediately declare all accredited Cuban diplomats in the United States persona non grata and, if Cuba does not take tangible action, close the U.S. Embassy in Havana," they wrote.
All five are members of the Senate Intelligence Committee, one of the congressional panels looking into the matter. Burr is its chairman and Cornyn is the number two Republican in the Senate.
President Donald Trump's fellow Republicans control majorities in both houses of the U.S. Congress.
The letter came as the United States was expected to issue new, tighter restrictions on Americans traveling to Cuba, as part of a partial rollback of the U.S.-Cuban detente by President Donald Trump. Rubio, a Cuban-American, was a key player in forging the new, more hostile policy towards the island.
The U.S. State Department did not immediately respond to a request for comment on the letter. The seaside U.S. embassy in Havana was still closed due to damage in the wake of Hurricane Irma, with staff working from the ambassador's residence and from home.
A source close to the investigation underway on the island said the Cubans had been very cooperative, even offering to let the FBI in to investigate for example.
"As far as we have ever known, the U.S. officials here in Cuba have never suspected the Cubans as perpetrating these events," the source said.
Foreign policy experts say it is hard to see what Cuba would have to gain from perpetrating attacks on diplomats. It has enjoyed good relations with Canada for many years and in 2014 started to normalise relations with its old Cold War enemy the United States.
Theories abound. One is that another country like Russia, Iran or North Korea might want to drive a wedge between Cuba and the west. Another is that there is an internal power struggle underway on the island.