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President Barack Obama held a bilateral talk with Cuban President Raul Castro on Tuesday, the second time they’ve met this year.

It came less than 24 hours after Castro delivered a blistering thinly veiled attack on the United States, condemning imperialism, and the U.S. control of the Guantanamo naval base, among other things.

The talk, which was not open to the media, is believed to have dealt with the lifting of the U.S.-Cuba embargo, which only the U.S. Congress can make happen, as well as other conditions that Castro laid out in his Monday speech.

Castro has said that in order for diplomatic relations to be truly and fully restored between the decades-long adversaries, the naval base must be returned to Cuba, technological programs the U.S. uses to emit messages to the people of the island must stop, and the U.S. must compensate Cuba for damages suffered as a result of the embargo.

Obama, who in December announced that that U.S. trade and travel restrictions would be dramatically eased, has been pushing for the embargo to end.

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The Tuesday meeting took place on the sidelines of the annual gathering of world leaders at the United Nations. Obama and Castro smiled and shook hands before beginning their private talks.

Since the two leaders made their surprise announcement about restoring relations last December, the two countries have reopened embassies in each other's capitals. But sharp differences remain, particularly over Cuba's human rights record and detainment of political prisoners. Both sides want Congress to lift a longstanding economic embargo against the communist island nation, but many Republican lawmakers and some Democrats want to keep it in place.

Cuba also seeks the return of land occupied by the U.S. Navy base at Guantanamo Bay; the U.S. says that is not in the plan.

In his address Monday at the opening of the U.N. General Assembly's annual ministerial meeting, Obama discussed the shift in policy toward Cuba and said he was confident that Congress "will inevitably lift an embargo that should not be in place anymore."

Ben Rhodes, a deputy national security adviser for Obama, said Castro's presence at the U.N. gathering is a signal "that we're in a new era."

Obama and Castro first spoke in December after the secret process to restore diplomatic relations was revealed.

They met in person in April while attending a regional summit in Panama. Before then, the last time a U.S. and Cuban leader had convened a substantive meeting was in 1958.

Obama and Castro spoke by telephone again earlier this month before Pope Francis visited Cuba and the United States.

Francis was a go-between for the U.S. and Cuba during their secret talks.

The Associated Press contributed to this report.

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