Republican lawmakers on Wednesday skewered President Obama’s announcement that the U.S. and Cuba have agreed to reopen embassies in each other’s capitals—with several vowing to block the confirmation of any U.S. ambassador to the communist country.

Critics, including several GOP presidential candidates, are arguing that the president – in ending 50 years of frozen relations – is rewarding Cuba’s dictatorial regime. Immediately after Obama announced what he called a “historic step forward,” Sen. Ted Cruz of Texas promised to oppose any ambassador to Cuba or funding for an embassy construction.

“I, for one, want the Cuban people to know that there are still those who stand with them, and who know the Castros for what they are,” said Cruz, a Cuban-American, in a statement. “I will hold any nominee President Obama sends to the Senate to be ambassador to Cuba, and I will work to disapprove any new funds for embassy construction in Havana, unless and until the President can demonstrate that he has made some progress in alleviating the misery of our friends, the people of Cuba.”

Sen. Marco Rubio of Florida issued a similar statement, arguing the Obama administration has “continued to look the other way and offer concession after concession.” Rubio, the son of Cuban immigrants, also said he intended to oppose the confirmation of any ambassador to Cuba until abuses of the Castro regime are addressed.