President Obama could visit Cuba before the end of his term in office, White House press secretary Josh Earnest said Thursday.

“I know there’s one person particularly that hopes President Obama will be in Havana at some point in the — at some point in the relatively recent future, and that’s President Obama himself,” Earnest said when asked by a Cuban reporter if the president had plans to visit Havana prior to leaving the White House in 2016.

Cuban officials met with their state department counterparts here Thursday in the fourth round of talks on reestablishing diplomatic relations and opening embassies in their respective capitals.

Late in the day, in an indication that progress may have been made, the State Department said negotiations would continue Friday, and both delegations scheduled morning news conferences.

One of the main sticking point in the negotiations has been whether U.S. diplomats will be able to move about the country without seeking prior government permission and meet with Cubans “who may not be a part of or even supportive of the Cuban government,” Earnest said.

Neither U.S. nor Cuban negotiators provided initial details on the outcome of Thursday’s talks, although both sides had expressed optimism as they began and confidence that embassy access issues eventually would be worked out.

Earnest’s suggestion that Obama might visit Cuba follows the president’s historic meeting with Cuban President Raúl Castro last month in Panama.

In the past Obama had played down the possibility that he might visit before leaving office. “With respect to Cuba, we’re not at a stage here where me visiting Cuba or President Castro coming to the United States is in the cards,” Obama told reporters in December. The president’s comments came shortly after he announced the first major change in Cuban policy in more than 50 years.

The president noted at the time that he was still “a fairly young man” and suggested that he might visit the island nation after he leaves office.

“There’s nothing specific where we’re trying to target some sort of visit on my part,” he said at the time.

It’s unlikely that Obama would visit Cuba until diplomatic ties had been reestablished and embassies were reopened. Obama would have to inform Congress at least 15 days before opening an embassy in Cuba, but a State Department official suggested that could be done even before a final embassy agreement is reached.

The ultimate “normalization” of relations — ending the U.S. trade embargo with Cuba — requires congressional action and could still be years away. Asked Thursday whether he favored lifting the embargo, House Speaker John A. Boehner (R-Ohio) said he had met this week with “members who were interested in stopping this progression toward normal relations with Cuba, until such time as the [Cubans] begin to make serious changes in terms of the way they run their country.” The administration, Boehner said, “keeps giving and giving and giving. But the Castro brothers . . . are doing nothing.”

Boehner’s remarks echoed those of lawmakers — primarily those of Cuban heritage — at a Senate Foreign Relations hearing Wednesday, including Sen. Robert Menendez (D-N.J.), who expressed “deep concern that . . . the administration continues to entertain unilateral concessions without in return getting agreement on fundamental issues that are in our national interest and those of the Cuban people.”

Sen. Marco Rubio (R-Fla.) said that allowing more U.S. citizens to visit the island — one of the executive actions Obama has already taken — would only fill the pockets of state-owned businesses controlled by the Cuban military.

Despite their meeting with Boehner, lawmakers who object to the opening have been unsuccessful in promoting legislation that would halt or limit the initiative.