But Tillerson said last week the United States is considering whether to close its embassy in Cuba following the alleged attacks, which USA authorities say began past year and continued to at least last month.
The White House has ruled out Cuba being responsible for the alleged "sonic attacks" which have supposedly affected 20-some diplomats, based on the assumption that any of this had actually happened.
Rep. Ed Royce (R., Calif.) who chairs the committee, then formalized the request for a briefing on the "sonic" attacks and the state of the US investigation into how and why they occurred.
"He stated that according to the preliminary results obtained by the Cuban authorities in their investigations, which have borne in mind the information given by the US authorities, there is no evidence so far of the cause or the origin of the health disorders reported by the USA diplomats", Cuba's embassy said in a statement.
Cuba's top diplomat also said that Havana's probe into the mysterious case had uncovered "no evidence so far of the cause or the origin of the health disorders reported by the United States diplomats".
Tillerson, for his part, told the visiting Cuban that the USA still has "profound concern" for the safety and security of its diplomats in Havana.
Nauert also confirmed that 21 of the diplomats experienced the attacks, which have left some victims experiencing permanent hearing loss, damage to their cognitive abilities, sleeplessness, and other serious symptoms. A USA official told CNN it seems clear Cuba has some involvement in the matter.
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.More news: Students stabbed in Bronx school
"We've had regular contact to register our deep concern with what's happened in Havana and to remind the Cuban government its obligation under the Geneva convention to protect our embassy employees and their families down there", Sullivan said.
Washington has not accused Cuba of being behind the attacks, but has repeatedly warned that Havana is responsible for the safety of foreign envoys on its soil, and in May, two Cuban diplomats were expelled from the US.
Deputy Secretary of State John Sullivan told Congress on Tuesday that it was a reasonable suspicion that Cuban authorities either were involved in the incidents or at least knew they were occurring.
Rodriguez told Tillerson in the Tuesday meeting that Havana "has never perpetrated nor will it ever perpetrate attacks of any kind against diplomats" and that it had implemented further measures to protect US Embassy staff since they reported the incidents.
That number could change, she said, noting that the tally has shifted upward as the USA government has medically confirmed the number of individuals impacted by the attacks.
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.
The U.S. has said the tally of Americans affected could grow as more cases are potentially detected.