Rubio said State's reply to Rubio on Saturday was essentially a non-answer.

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"Then I got this letter today that, to summarize, basically says: 'Thank you for your letter, but we can't talk to you about it,' " Rubio said. "That is not what I expected to get, and so we are going to hold those nominations again until we take this seriously.

"This is a problem," he added. "We have these companies in America that are advertising tourism to Cuba — tourism that is not just a source of irritation, it is a source of hard currency."

Rubio's office said that the two nominations he would hold are those of Roberta Jacobson to be assistant secretary of State for the Western Hemisphere, and Adam Namm to be Ambassador to Ecuador.

Cuban Americans like Rubio have long argued that allowing travel to Cuba allows Americans to bring hard dollars to the island, which the Cuban government can then harvest by forcing Cuban residents to buy goods in dollar stores.