Tillerson's public schedule for Tuesday shows a meeting with Cuban Foreign Minister Bruno Eduardo Rodriguez Parrilla at 5 p.m.at the State Department.
Secretary of State Rex Tillerson plans to meet with Cuba's top diplomat Tuesday evening in Washington just days after US officials expressed an "urgent need" to unravel the mystery of the "sonic" attacks on USA diplomats in Havana.
Cuba has denied any involvement in the incidents, which have threatened its already fragile detente with its northern neighbor.
"The Foreign Minister reaffirmed that the investigation to resolve this matter is still in progress", the Cuban Foreign Ministry said in a statement, noting that "effective cooperation" of USA authorities was essential.
The U.S. State Department said the conversation was "firm and frank" and Tillerson "conveyed the gravity of the situation and underscored the Cuban authorities' obligations to protect Embassy staff".
Tillerson said a week ago that closing the embassy was "under evaluation".
Relations between the United States and Cuba were restored by then president Barack Obama and his counterpart Raul Castro in 2015, half a century after the Cold War rivals cut ties and began a long diplomatic standoff.
The Cuban Embassy in Washington says Cuba has investigated and found no evidence to explain who or what is causing health damage to American diplomats in Havana.
"No one believes that the Cubans are responsible", a source told McClatchy.
Cuban officials were not as diplomatic in their assessment of the current state of U.S. Cuba keeps tight surveillance on American diplomats in the country and would be likely to know if something significant were happening to them. In his United Nations speech last week, Rodriguez said early results from Cuba's own investigation have "found no evidence whatsoever that could confirm the causes or the origin" of the incidents, implicitly casting doubt on the USA version of accounts.
Yet while the US has avoided blaming Cuba directly for the incidents, the growing public outrage has forced both countries to adopt a tougher tone.
Last week, US diplomats held another high-level meeting with Cuba amid concerns about the incidents. Several U.S. lawmakers have called on the Trump administration to expel all Cuban diplomats from Washington.
Tillerson recently said that the United States is considering closing its embassy in Cuba after some 20 diplomats suffered mysterious health problems in recent months, including minor cerebral lesions or loss of hearing caused by supposed sonic attacks. Some have been diagnosed with mild brain injury and permanent hearing loss.
US authorities are baffled as to whom is behind the attacks and what exactly is causing the unusual symptoms, although a sonic weapon of some sort is suspected.
The U.S. has said the tally of Americans affected could grow as more cases are potentially detected.
The meeting - the first between the two men since Donald Trump entered the White House in January - took place behind closed doors, the US State Department said.