Cuban President Raul Castro has told the UN that normal relations with the US will only be possible if America takes a number of measures including the abolition of its trade embargo.
He said it was also necessary for the US to return the military base at Cuba's Guantanamo Bay and end anti-communist broadcasts to the island.
US President Barack Obama also called for the trade embargo to be lifted.
He said that he was confident that the US Congress would do so soon.
The two leaders are expected to meet later on Tuesday in New York.