Rubio and Sen. Bob Menendez, D-N.J., have submitted an amendment blocking any new flights from U.S. airports to Cuba that might be allowed under President Barack Obama's plan, the Spanish-language Miami daily El Nuevo Herald reported.
The amendment was added to a funding bill for the Federal Aviation Administration blocking any new U.S. flights to countries on the list of supporters of international terrorism. Cuba, Iran, Syria and Sudan are on that list.
"There is no reason for the United States to help enrich state sponsors of terrorism," Rubio said.
Obama set the stage for a fight over travel to Cuba last month when the White House announced plans to make it easier for U.S. educational, religious and humanitarian groups to visit the Communist Caribbean island.