Making good on a pledge to change U.S. posture toward Cuba, President Barack Obama held 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 to help fostering greater economic freedom on the island.

The White House said the leaders discussed additional steps each government can take to deepen cooperation. Obama also reiterated U.S. support for human rights in Cuba, a sticking point in the relationship, the White House said.

Cuban Foreign Minister Bruno Rodriguez focused on the pace of normalizing relations following the meeting, saying speeding up the process will require Obama using his executive authority to substantially modify the decades-old U.S. economic embargo.

Rodriguez said actions Obama has taken so far “have a very limited value, a very limited scope and do not deal with any significant aspects when it comes to the implementation of the blockade against Cuba.”

But many Republican lawmakers, and some Democrats, oppose lifting the embargo at this stage.

Obama and Castro 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 and the economic embargo. Cuba also insists on 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 new approach toward Cuba and said he was confident that Congress “will inevitably lift an embargo that should not be in place anymore.”

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.

Obama also met Tuesday with Nursultan Nazarbayev, the president of Kazakhstan.

(AP)