Making good on a pledge to change U.S. posture toward Cuba, President Obama opened talks Tuesday with Cuban President Raul Castro, the second time the leaders of the once-estranged nations have met this year. 

Obama and Castro smiled and shook hands before beginning their private talk on the sidelines of the annual gathering of world leaders at the United Nations. 

The encounter comes as the Cold War adversaries go about the long and complex process of normalizing relations following decades of animosity. The U.S. recently eased rules for citizens who want to visit or do business in Cuba, a step aimed at fostering greater economic freedom on the island. 

Both leaders surprised the world last December by announcing they had agreed to restore diplomatic relations. 

Since then, 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.