Cuba's top diplomat has warned the United States against taking hasty decisions over alleged incidents that have harmed US embassy staff in Havana, and urged its authorities to cooperate on the investigation into the mysterious affair.

Key points: Cuba warns US against making hasty decision about Havana embassy

Cuba warns US against making hasty decision about Havana embassy Several US diplomats have been struck with mysterious illnesses

Several US diplomats have been struck with mysterious illnesses Alleged "acoustic attacks" are being investigated

Sixteen Americans linked to the US embassy in Cuba sustained physical symptoms after mysterious "incidents" started happening late last year.

The incidents were previously described as "acoustic attacks".

Several embassy staff members returned to the US with hearing problems and other symptoms including headaches, nausea and balance disorders.

Cuban Foreign Minister Bruno Rodriguez called for Tuesday's meeting with US Secretary of State Rex Tillerson in Washington to discuss the case, which has been threatening the already-fragile detente between the two former Cold War foes.

The highest level meeting to take place between the two countries since US President Donald Trump took office, came 10 days after Mr Tillerson said the United States was considering closing its recently reopened embassy in Havana.

"The Foreign Minister reaffirmed that the investigation to resolve this matter is still in progress," the Cuban Foreign Ministry said in a statement, noting "effective cooperation" of US authorities was essential.

"It would be regrettable that a matter of this nature is politicised and that hasty decisions not supported by conclusive evidence and investigation results are taken."

The Cuban Foreign Ministry said the meeting, "took place in a respectful ambiance".

The US State Department said the conversation was "firm and frank" and Mr Tillerson, "conveyed the gravity of the situation and underscored the Cuban authorities' obligations to protect embassy staff".

Washington has not yet blamed Cuba

Earlier this year, Washington expelled two Cuban diplomats over the alleged incidents, which it says caused symptoms from hearing loss to nausea in US embassy staff and their families in Havana, although it has so far not laid blame on Cuba.

Cuba reiterated on Tuesday it, "has never perpetrated nor will it ever perpetrate attacks of any kind against diplomats", and said it had implemented additional measures to protect US personnel since they reported the incidents.

The case has brought simmering tensions between the two countries since Mr Trump took office to the boil.

Mr Trump, who in June vowed to partially roll back the detente with Cuba agreed by predecessor Barack Obama, called the Communist-run nation "corrupt and destabilising" in his address to the United Nations General Assembly last week.

He said he would not lift the US trade embargo on the Caribbean island until it made "fundamental reforms". Cuba described his comments as "unacceptable and meddling".

Donald Trump speaks at a news conference in Washington. ( AP: Pablo Martinez Monsivais )

Experts agreed it was hard to see how any attacks could have been carried out or what the motivation could be.

Theories abound, from surveillance technology gone awry to a sophisticated acoustic weapon in the hands of Cuban-American exiles or third-party state actors such as Russia, Iran or North Korea, but most flounder.

Audiologists, for example, have raised doubt over the possibility of whether any sonic weapon existed that could be used covertly to bring about the range of symptoms mentioned by diplomats.

Reuters