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Menendez's floor speech on Monday came after Jorge Luis García Pérez, known as "Antúnez," was reportedly severely beaten Saturday for testifying about repression under Cuba's Communist regime. 

"The arrest and beating of Antúnez, clearly as a result of his Senate testimony, is further proof of the continuing brutality of the Castro brothers' regime and further evidence of the need for the United States and other Democratic nations to stand up against tyrants and realize that the nature of the regime won't be altered by increasing tourism to the island," Menendez said. "Today I am calling on the State Department to cease providing any non-essential visas for travel to the United States by Cuban officials."

Menendez continued, "I'm also calling on the United Nations Committee on Human Rights and the United Nations Committee on Torture, which last week on its own called on Cuba to answer for its dramatic increase in arrests, to immediately investigate this incident.

"Make no mistake, this was not a bureaucratic arrest, not a random act of violence by the regime.

"This was a deliberate violation of human rights, in my view, authorized at the highest level of the regime as punishment simply because Antúnez had the courage to speak truth to power."

Antúnez and three other Cuban dissidents testified before the Senate Foreign Relations Committee last week via video. Menendez and Sen. Marco RubioMarco Antonio RubioThe Memo: All eyes on faltering Biden ahead of first debate GOP lawmaker on Iran: Congress should vote on 'what's worthy of spilling American blood and what isn't' The Memo: Can Trump run as an outsider? MORE (R-Fla.), who both disagree with the Obama administration's policy of expanding travel to Cuba, called for the hearing.

Earlier on Monday, Rubio issued a statement in response to the report about Antúnez.

"Antúnez is a courageous human-rights activist. It is clear that he has been jailed and savagely beaten by criminals working for the Castro regime because he testified before the Senate last week," Rubio said in a statement. "The regime’s thugs will eventually be held accountable for these crimes. History will not wipe away the blood they have on their hands."