Cuban Foreign Minister Bruno Rodríguez speaks during the 72nd General Assembly at the United Nations in New York on Sept. 22. (Timothy A. Clary/AFP/Getty Images)

Secretary of State Rex Tillerson met with Cuban Foreign Minister Bruno Rodiguez on Tuesday evening to discuss the still-mystifying health problems that have befallen U.S. diplomats stationed in Havana.

In a lengthy account of the meeting, Cuba’s Foreign Ministry said Havana has been conducting its own investigation into the incidents, on orders from “the top level of the Cuban government,” a reference to President Raúl Castro. But it said Cuba so far had found no evidence pointing to the cause or origin of the health disorders that have affected at least 21 Americans connected to the embassy. Nevertheless, it said measures had been taken to protect diplomats still stationed in Havana and their families, without specifying what they are.

U.S.-Cuba relations, already tense since President Trump vowed to reverse the rapprochement undertaken by the Obama administration, have been weakened further by the case of the injured diplomats. Some have suffered hearing loss and traumatic brain injury. Investigators are looking into the possibility they were subjected to some sort of "sonic attack."

Cuba has vehemently denied being involved in any way, raising speculation a third country may be responsible. But two months after the State Department publicly acknowledged the incidents, they are no closer to solving what happened, much less who did it.

In a brief account of the meeting, State Department spokeswoman Heather Nauert characterized the conversation as a “firm and frank” discussion of U.S. concern 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,” Nauert said.

The end-of-the-workday visit by Rodriguez to Tillerson's office, requested by the Cubans primarily to discuss the incidents, appeared to be an effort to persuade Tillerson not to close the embassy in Havana, a step he said recently that he is considering.

The Cubans also signaled their concern they are being blamed for the diplomats’ injuries before investigations are complete and urged “effective cooperation” between Cuban and U.S. authorities looking into the case.

Rodriguez, they said, “also stated that it would be regrettable that a matter of this nature is politicized and that hasty decisions not supported by conclusive evidence and investigation results are taken.”

The meeting between Tillerson and Rodriguez represented the highest-level meeting of officials from the two countries during the Trump administration. However, it comes at the lowest point in U.S.-Cuba relations since the countries put aside half a century of enmity and normalized relations under the Obama administration in 2015. Trump has said he wants to reimpose restrictions that would limit U.S. business dealings in Cuba and make it harder for Americans to visit except on organized tours.

In a speech at the United Nations last week, Trump called the Cuban government “corrupt and destabilizing” and vowed not to ease the U.S. trade embargo against the island until democratic reforms are made. The Cubans called his remarks “disrespectful, unacceptable and meddling.”

Despite the ideological differences, the State Department has said Cuba has cooperated in facilitating the investigation into what harmed the envoys from the United States, and several Canadians as well.

The complaints of health issues began in the final months of the Obama administration and continued into the Trump administration. Many of those injured have left the country for treatment.

In May, the United States expelled two Cuban diplomats from Washington as a response. The State Department did not publicly reveal the expulsions, or the reason behind it, until August.

According to the Cuban account, Rodriguez told Tillerson the expulsions were “unwarranted” and said Cuba’s record in protecting diplomats is “impeccable.”

“He reaffirmed that the Cuban government has never perpetrated nor will it ever perpetrate attacks of any kind against diplomats,” the statement said. “The Cuban government has never permitted nor will it ever permit the use of its territory by third parties for this purpose.”

Rodriguez also told Tillerson he hopes the fact U.S. diplomats were injured while serving in Cuba does not damage already difficult relations. The Foreign Ministry said he expressed to Tillerson Cuba's desire to continue bilateral dialogue on issues "based on respect and sovereign equality, despite the profound differences that exist between the two countries."