MIAMI — Cuban-Americans nationwide are almost evenly divided over support for the embargo and for President Obama’s effort to normalize relations with Cuba, according to a new poll that shows a vast generational divide in reaction to this week’s historic announcement.

The poll by Bendixen & Amandi International also showed that Cuban-Americans are nearly split on whether Obama should have exchanged prisoners Wednesday with Raul Castro’s communist government.

But they strongly disapprove of Obama’s foreign policy overall and his approach to Cuba specifically, according to the poll of 400 Cuban-Americans conducted for The Miami Herald, El Nuevo Herald and the Tampa Bay Times.

Among the strongest responses from Cuban-Americans: Whether the United States should remove Cuba from the State Department’s list of state sponsors of terror. That move is opposed by 60 percent, with only 22 percent in favor. The Obama administration is reviewing Cuba’s designation.

“The Cuban people will not see any benefits,” poll respondent Gabriel Rivera, a 40-year-old Miami resident, said of Obama’s announcement. “They will remain in the same condition because the Cuban government doesn’t grant any freedoms.”

Rivera, a nurse practitioner, left behind family in Cuba in 2004 when he emigrated from Havana to the United States. A registered Republican, he said voters like him “won’t forget, even after five, six, eight years, that Obama betrayed the history of the Cubans who have fought for Cuban freedom.”

The profile of those most likely to disapprove of Obama’s positions and more-normalized relations with Cuba: Republicans, those over 65 and those born in Cuba who emigrated to the U.S. before the 1980 Mariel boatlift crisis. After Mariel, immigrants from Cuba have tended to be considered economic immigrants, instead of political exiles.