Four rounds were held but the talks were suspended again in 2011 after Alan Gross, a U.S. Agency for International Development subcontractor, was sentenced to 15 years in prison for giving Cuban Jews sophisticated communications equipment paid for by a USAID pro-democracy program.

The most recent talks on direct mail were held in September 2009 — the year the Obama administration lifted travel restrictions for Cuban-Americans and limits on their money transfers to the island. Bisa Williams, then U.S. deputy assistant secretary of state for Western Hemisphere Affairs, met with Cuban officials in Havana to discuss technical aspects of resuming direct mail service.

At the time, the relationship between Havana and Washington seemed to be warming.

But the arrest of Gross in December 2009 and his subsequent conviction froze any further opening toward Cuba, although the Obama administration further tweaked travel restrictions in 2011 by reviving and expanding people-to-people cultural trips to Cuba for Americans.

Although the U.S. government has pressed for the release of Gross, Havana has seemed more interested in a swap for the release of five Cubans convicted in 2000 of spying on anti-Castro groups in Miami and military installations. Federal prosecutors contended the men’s spying led to the shoot-down of two Brothers to the Rescue planes, killing four members of the exile group in 1996. The Cuban government, meanwhile, considers USAID pro-democracy programs to be subversive.

Cuban observers say the stalemate over Gross has been an obstacle to any further opening with Cuba despite recent Havana’s recent travel and economic reforms.

Although the Cuban Democracy Act, which Congress approved in 1992, is generally thought of as tightening the embargo, it does contain provisions in support of the Cuban people and directs the U.S. Postal Service to “take such actions as are necessary to provide direct mail service to and from Cuba.’’

“We’re hopeful that we’ll be able to move things forward,’’ said spokeswoman Jen Psaki at a U.S. State Department briefing the day before the direct mail talks began.

But Florida Republican Rep. Ileana Ros-Lehtinen said the mail talks aren’t in the interest of the United States. She also predicted the migration talks would go nowhere.

“There is no reason to have this talk because the ones not complying with the mail accords from years ago are the Castro thugs,’’ she said in a statement. “The regime is once again manipulating the U.S. administration in this game because it wants us to lift the embargo and make further concessions. Meanwhile, a U.S. citizen languishes unjustly in a Cuban prison and brave freedom Cuban activists are risking their lives while on hunger strikes to protest the island tyranny.”

Mauricio Claver-Carone, director of the pro-embargo U.S. Cuba Democracy Political Action Committee, concurred. “We look forward to the day the Obama administration stops rewarding the Castro regime for taking an American hostage and for its dramatic increase in repression.”

However, Pepe Hernández, president of the Cuban American National Foundation, said his exile organization favors the mail talks. “It’s been our position for quite some time that we favor anything that improves the relationship with the people of Cuba,’’ he said.

“It’s interesting that the Cuban government is now willing to sit down for these talks,’’ said Hernández.

Advocates of improving relations with Havana have been urging the White House to remove Cuba from the U.S. list of countries that support international terrorism as an opening gambit for Gross’ release.

Wayne Smith, a former head of the U.S. Interests Section in Havana and now director of the Cuba project at the Center for International Policy, said he had hoped that the Obama administration would have taken steps beyond the mail and migration talks to repair the tattered relationship with Havana. But he added, “It’s something.’’

The 2009 measures to open travel and remittances for Cuban-Americans were far more significant, Smith said.