WASHINGTON - The United States on Friday ordered more than half of the staff at the US embassy in Havana to leave and warned against travels to Cuba, following mysterious "incidents" that caused health problems for American diplomats, US media reported.

The US embassy in Havana will continue to operate with a reduced staff. It will stop processing visas indefinitely, according to US media reports.

The move came after US authorities confirmed last month that at least 21 Americans working at the embassy in Havana had suffered physical debilitations.

No details of the injuries have been released, but media reports said the affected Americans incurred severe hearing loss and at least one victim suffered some "brain damage".

The move will deal a blow to the delicate ties between the US and Cuba. The former Cold War rivals resumed their diplomatic relations in July 2015 after more than five decades of hostility.

US President Donald Trump in July announced new restrictions on US leisure travel to Cuba and US business with Cuban military, in a move to cancel what he called his predecessor Barack Obama's "one-sided deal" with Cuba.

On Tuesday, US Secretary of State Rex Tillerson met with Cuban Foreign Minister Bruno Rodriguez to discuss the incidents. It was the highest-level diplomatic contact between the two countries since Trump became US president in January.

US State Department spokesperson Heather Nauert said the two top diplomats had a "firm and frank" discussion of US concerns for its employees.

"The secretary conveyed the gravity of the situation and underscored the Cuban authorities' obligations to protect embassy staff and their families under the Vienna Convention," she said.

The United States expelled two Cuban diplomats in late May over the incidents. Cuba said it was investigating the incidents.

"Cuba has never, nor would it ever, allow the Cuban territory to be used for any action against accredited diplomatic agents or their families," the Cuban Foreign Ministry said in a statement.