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By Andrea Mitchell, Katie Wall and Abigail Williams

American and Cuban officials who met on Thursday in Washington D.C. for a fourth round of talks are nearing an agreement on fully restoring diplomatic ties and opening embassies — a step toward thawing icy relations in place since the Cold War era.

The talks were led by two diplomats. U.S. Assistant Secretary of State Roberta Jacobson and Josefina Vidal, director of U.S. affairs at the Cuban foreign ministry met to discuss some of the finer details.

Some of the larger points of contention, such as Cuba’s demands for banking privileges in the U.S. have been resolved. The U.S did not acknowledge linkage of banking privileges to normalization of relations, but it was clearly an obstacle from the Cuban perspective.

Cuba announced on Thursday that Stonegate, a small bank in Florida, is the first U.S. financial institution to take their account.

“The adoption of banking services will ease the burden on the Cuban Interests Section in terms of issuing travel visas and other functions associated with any embassy in Washington, D.C.” Stonegate president Dave Seleski said in a statement. “ We hope this is the initial step to normalize banking ties between the two countries, which will benefit American companies wanting to do business in Cuba, as well as the Cuban people."

The State Department sees the move as a good sign.

“I'm trying not to sound too Pollyannaish as I go into the fourth one,” a senior State Department official told reporters this week in a background briefing. “But I do think we're closer than we have been in the past, and I think my counterparts are coming up here with a desire to get this done.”

Last month, the Obama administration removed a major obstacle toward normalization of relations when it recommended to Congress that Cuba be removed from the list of countries the U.S. considers sponsors of terrorism. The highly anticipated move followed a historic meeting between President Barack Obama and Cuba President Raul Castro in Panama at the Summit of the Americas.

The terror designation gets lifted at the end of this month, unless Congress takes action to block it, which is not expected.

Cuban journalists attending the White House press briefing on Thursday asked press secretary Josh Earnest if the president planned to visit Cuba. Earnest welcomed them to the briefing room and said the president is hopeful about a future visit.

"I know there's one particular person who hopes that President Obama will be in Havana at some point in the relatively recent future, and that's President Obama himself,” Earnest said. “ I know that he would relish the opportunity to visit the island of Cuba and Havana in particular."

But there are still some sticking points before the two sides can agree to re-opening embassies.

Officials must hammer out an agreement on security requirements outside the proposed embassy in Havana. Both countries limit movement.

Cuban diplomats are restricted to a 25 mile radius as well and must ask permission to venture beyond that distance. This applies to both Cuban diplomats in Washington D.C. at the "Interests Section" as well as Cubans stationed at the embassy at the United Nations.

A particular sore point for Castro is an American program in Havana that offers computer courses to Cubans aimed at training them to be journalists. Castro has called the program, which is taught by American journalism professors, “illegal” in a nation where media is state controlled and Cuban officials have said there is no authority under the Vienna Conventions for diplomats to permit this kind of training.

The State Department said the program is fairly standard, but did not rule out possible changes.

Should the two nations strike an agreement, the State Department would give Congress 15 days’ notice before re-opening the embassy. Congress cannot block this action since there is precedent for this being the prerogative of the president and no new appropriations are involved.

Opponents in Congress have no recourse and some lawmakers are none too happy about that.

The Senate Foreign Relations Committee hearing on Cuba policy was relatively civil on Wednesday until New Jersey Democrat Sen. Bob Menendez pressed Jacobson over the Obama administration's decision to normalize relations.

"I don't get it," Menendez said. "We have gotten nothing in return. But the Cubans have gotten plenty in return. And if that's our way of negotiating, then we have a real problem on our hands."

Republican Presidential candidate Marco Rubio, R-Fla. also expressed his frustration with the Cuba policy, and launched a panel-wide debate after he alleged that American tourists' dollars will inevitably end up in the hands of the Cuban military, who own a large percentage of the country's hotels.

“What we're really talking about is increased business ties to Cuban military,” Rubio said.

Jacobson acknowledged his point but pointed to signs of increased competition.

“It's accurate to say Cuban military run large percentage of Cuban hotels,” she said. “But we also have private entrepreneurs moving into area, like Airbnb.”