MIAMI — For Amaury Villa, who arrived here from Cuba more than 15 years ago and became a permanent resident, pleading guilty in 2012 to federal charges that he sold stolen prescription drugs was a difficult choice. But there was one positive aspect: Unlike most foreign citizens convicted of serious crimes, Mr. Villa stood next to no chance of being deported back to his home country.

The United States cannot deport him or the vast majority of the 34,500 other Cubans who face orders of deportation, almost all of them for criminal offenses, because Cuba will not accept them back. Instead, after serving his sentence, Mr. Villa will be allowed to return to his community in South Florida.

But as President Obama re-establishes diplomatic ties with Cuba after more than five decades, one priority for the administration is persuading Cuba to take back Cuban citizens who have been ordered deported, a longstanding concern for the United States, said a senior administration official who declined to be identified because the official was not authorized to speak on the record.

When Cuban and American officials meet this week in Havana to discuss migration issues, the deportation issue will be on the agenda, as it has been in the past, the official added.