Homeland Security Secretary Alejandro Mayorkas faced heavy blowback for declaring Tuesday that those fleeing violence in Cuba or Haiti by sea would not be allowed into the U.S. -- and would either be returned or referred to a third country.

"The time is never right to attempt migration by sea," Mayorkas said at a news conference on Tuesday. "Allow me to be clear: If you take to the sea, you will not come to the United States."

Social media critics erupted Wednesday, leveling strong accusations against the Biden administration for closing the doors to Cubans and Haitians fleeing violent political uprisings in their country while maintaining exceptionally lax immigration restrictions at the US-Mexico border.

"Biden's DHS Secretary, Alejandro Mayorkas PROVES his goal is to open the borders to illegal immigrants who are likely to vote Democrat, while slamming the door on anti-communist Cuban refugees who are likely to be future Republicans," Dinesh D'souza wrote Wednesday.

"DHS Secretary Mayorkas does not want legitimate asylum-seekers fleeing Cuba to come to the US despite his family having done just that,"  Donald Trump Jr. wrote Wednesday. "Apparently he only wants people pretending to need asylum because those people will still vote for socialist Democrats!"

"DHS secretary Mayorkas (Cuban immigrant who fled with his family in 1960) says no refuge for Cubans fleeing the country," a conservative pundit who goes by the handle Suburban Black Man wrote. "I wonder why... Could it be because they are likely to naturalize, seek citizenship, and vote AGAINST all of the commie bulls--- the Democrats are pushing?"

Texas Republican Rep. Lance Gooden wondered why Mayorkas doesn't say "this to illegals crossing our southern border?" 

Other users noted that Mayorkas's own family fled Cuba in 1960 when he was just a year old.

"Mayorkas is a Cuban national whose family fled to the United States and Florida. Do you think a single cable news host like Cuomo, Tapper or Chuck Todd will ask him about this? Just one?," the Spectator contributor Stephen L. Miller wrote.

Independent journalist Jordan Schachtel said it is "sickening" that Mayorkes is "denying others the opportunity that was presented to him when he was a kid. I can only imagine the betrayal that his fellow Cuban-Americans feel."

Mayorkas said that the Coast Guard is monitoring for activity that indicates increases in illegal migration across the Florida Straits. He warned that the waters are dangerous, particularly during hurricane seasons -- and that 20 people had died in the waters in recent weeks.

Mayorkas said that the U.S. is looking at parole programs for people in those countries—programs that were suspended by the Trump administration. But he said that those caught at sea would be either returned or moved to a different country—but not the United States. 

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"They are returned by vessels of interdiction. If individuals establish a well-founded fear of persecution or torture, they are referred to third countries for settlement," he said. "They will not enter the United States."