WASHINGTON—President Barack Obama backed the removal of Cuba from the list of state sponsors of terrorism, a critical move toward restoring diplomatic relations.

Havana will still face a variety of sanctions after it is removed from the list, but the step will likely prompt renewed interest from businesses and banks wary of entering the Cuban market.

Mr. Obama made a formal recommendation to Congress, setting in motion a 45-day review process during which lawmakers can take steps to block the move. However, Congress isn’t expect to block it and lawmakers would have to enact a joint resolution to do so, which Mr. Obama could then veto.

The president’s shift sets the stage for the two countries to formally reopen their embassies. But additional steps to normalize relations, such as further easing travel and trade restrictions, will require congressional action.

Mr. Obama met over the weekend in Panama with Cuban President Raúl Castro, the first summit between the two countries in more than 50 years.