"Cuba strictly abides by its obligations under the Vienna Convention on the protection and integrity of diplomats, an area in which it keeps an impeccable record", the Cuban ministry added in a statement summarizing Parrilla's talks with Tillerson.
Nauert on Tuesday confirmed that the Cubans had asked for the meeting. 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 US version of accounts.
The meeting was the first highest-level diplomatic contact between the two countries since Donald Trump became US president in January.
Yet while the USA has avoided blaming Cuba directly for the incidents, the growing public outrage has forced both countries to adopt a tougher tone.
During her daily press briefing Tuesday, Nauert confirmed that Tillerson was considering shuttering the USA diplomatic post, which would rollback Obama-era efforts to normalize relations with the island nation.
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.
They haven't been so successful with their "Cuban sonic weapons" because ordinary people are a little more suspicious, scientists question the existence of such weapons and because Cuba wasn't interested in doing anything like that while they were in negotiations with Obama.
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.
El Nuevo Herald reported that officials in the White House do not believe the Cuban regime was responsible for the alleged sonic attacks against U.S. diplomatic personnel in Havana. He also reaffirmed that at the suggestion of the highest level of the Cuban government it is initiated a priority search from the very moment the facts were reported, and additional measures were taken to protect USA diplomats and their families.
"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 statement read.
The Cuban government said it "rigorously fulfills its obligations ... of protecting the integrity of diplomats, in which it has an impeccable record", and reiterated that it considers "the decision of the United States government of withdraw two Cuban diplomats from Washington and the argument used to do so 'unjustified'".
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.
But Tillerson said last week the United States is considering whether to close its embassy in Cuba following the alleged attacks, which U.S. authorities say began previous year and continued to at least last month.
Sullivan assured him that the State Department would give him the information he needs. USA investigators have pursued the possibility the attacks were carried out with some sort of sonic device but have been unable to determine the cause or a culprit.