MIAMI — In the wake of President Obama’s move to rekindle diplomatic ties with Cuba, Cuban-American legislators in Washington and local officials in Florida are calling for reconsideration of a once-sacrosanct element of American foreign policy — the 1966 law that gives Cubans broader protections than any other immigrants arriving in the United States.

Critics of the law, joined by the hard-line Cuban-American congressional delegation, say it is being abused by recent waves of Cuban arrivals who regularly travel back and forth between Cuba and the United States as economic, not political, refugees.

Written during the height of tensions with the Soviet Union, the Cuban Adjustment Act was meant to offer safe haven for Cuban refugees fleeing oppression from their Communist government. The law allows all Cubans who reach the United States, legally or illegally, to become permanent residents in a year and a day. Five years later, they can become United States citizens.

The law is still popular with most Cubans in Florida. But influential Cuban-American politicians argue that the moves to normalize relations undercut the rationale for the law — that it protected refugees from an outlaw government at a time they did not have the option of returning home.