Supporters say it is a justified measure against a repressive Communist government that has never stopped being a thorn in Washington’s side. Critics call it a failed policy that has hurt ordinary Cubans instead of the government.

All acknowledge that it has not accomplished its core mission of toppling Fidel Castro or his brother and successor, Raúl.

“All this time has gone by, and yet we keep it in place,” said Wayne Smith, who was a young American diplomat in Havana in 1961 when relations were severed and who returned as the chief American diplomat after they were partially re-established under President Jimmy Carter. “We talk to the Russians, we talk to the Chinese, we have normal relations even with Vietnam,” Mr. Smith said. “We trade with all of them. So why not with Cuba?”