Secretary of State Rex Tillerson will meet Tuesday with Cuba's top diplomat, U.S. officials said, as the United States is seeking answers about mysterious "attacks" on its diplomats in Havana.

Tillerson's meeting with Cuban Foreign Minister Bruno Rodriguez is believed to be the highest-level diplomatic contact between the two countries since the start of President Donald Trump's administration in January. It comes as the delicate rapprochement between the longtime foes, started under President Barack Obama, is being jeopardized by mounting alarm over the diplomats' illnesses.

The meeting at the State Department will follow a speech Rodriguez delivered at the United Nations last week in which he harshly criticized Trump and his administration's policy toward the communist island. In a bid to show it's a good neighbor, Cuba has also offered to send doctors and humanitarian aid to Puerto Rico to help the U.S. respond to Hurricane Maria.

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For months after U.S. diplomats started falling ill in Havana, the U.S. and Cuba sought to prevent the issue from becoming an overriding irritant in the relationship. Neither country disclosed publicly that the incidents were occurring, even after Washington in May expelled two Cuban diplomats to protest Havana's failure to protect Americans on its soil.

Yet while the U.S. has avoided blaming Cuba directly for the incidents, the growing public outrage has forced both countries to adopt a tougher tone. Tillerson has said that closing the newly re-opened U.S. Embassy in Havana is under consideration, and several U.S. lawmakers have called on the Trump administration to expel all Cuban diplomats from Washington.

Embassy workers have complained of nausea, headaches, exhaustion and trouble concentrating and remembering words, and some have been diagnosed with mild traumatic brain injury and permanent hearing loss, according to the American Foreign Service Association and medical records examined by CBS News.

CBS News reported earlier that the top official in charge of security at the embassy was among those injured. CBS News is not naming the Regional Security Officer, who was scheduled to undergo medical treatment, according to a source. When contacted by CBS News, the individual declined to comment.

Meanwhile, the latest development illustrates how far-reaching the attacks have been, affecting one of the most senior leaders of the U.S. embassy that only reopened in 2015. CBS News Radio broke the story last month.

Cuba has denied any knowledge or involvement. In his U.N. 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 U.S. version of accounts.

"It would be unfortunate if a matter of this nature is politicized," said Rodriguez, who has represented Cuba on the world stage for years.

Last week, U.S. diplomats held another high-level meeting with Cuba amid concerns about the incidents. That meeting at the State Department included Cuban official Josefina Vidal, who has been the public face of Cuba's diplomatic opening with the U.S., and other Cuban officials.

Of the 21 medically confirmed U.S. individuals affected — diplomats and their families — some have permanent hearing loss or concussions, while others suffered nausea, headaches and ear-ringing. Some are struggling with concentration or common word recall, The Associated Press has reported.

The U.S. has said the tally of Americans affected could grow as more cases are potentially detected. The State Department has emphasized that the U.S. still doesn't know what has occurred.