President Barack Obama met his Cuban counterpart Raul Castro on Tuesday at the United Nations, where a day earlier both had called for an end to the American trade embargo against Havana.
The leaders of the former Cold War rivals shook hands at the start of what was their second meeting, after their historic encounter in April at the Summit of the Americas in Panama.
Close neighbors but long-time foes, the United States and Cuba restored diplomatic ties in July after a five-decade stand-off.
The two countries have re-opened their embassies in each other's capitals and are engaged in a dialogue to resolve their remaining political differences, but the economic sanctions remain.
Obama's White House wants to lift the embargo, which prevents almost all trade across the Florida Straits, but conservatives in the US Congress are not ready to forgive the communist island.
On Monday, during a speech to the UN General Assembly, Obama said he was confident Congress would "inevitably lift an embargo that should not be in place anymore."
He acknowledged that Washington's Cuba policy had "failed to improve the lives of the Cuban people" but stressed that human rights remain a concern in relations with Havana.
Castro, who succeeded his brother Fidel in 2006, made his first address to the Assembly a few hours after Obama took the podium.
"Now a long and complex process begins towards the normalization of relations, but this will only be achieved with the end of the economic, commercial and financial blockade," he said.
At a UN development summit on Saturday, Castro called the embargo the "main obstacle" to his country's economic development.
Next month, the General Assembly will discuss a new draft resolution condemning the US embargo against Cuba.
The assembly has voted each year since 1982 to approve a resolution calling on the United States to lift the embargo.