Cuba wants to re-establish relations with the United States with a focus on humanitarian and other issues, its foreign minister has said.
Bruno Rodriguez also called on President Barack Obama to release five Cubans serving US espionage sentences, telling the opening of the new United Nations General Assembly that the continued imprisonment of the five men convicted of spying in 2001 was "inhumane".
The Cuban government refers to the five men as heroes who were gathering information about terrorist groups in the United States to protect their homeland.
The foreign minister said the two countries had many points of understanding in common.
"The Cuban government reiterates its willingness and interest to move towards the normalisation of relations with the United States," Mr Rodriguez said.
"I reiterate the proposal of beginning a dialogue aimed at solving bilateral problems, including humanitarian issues, as well as the offer of negotiating several co-operation agreements to combat drug-trafficking, terrorism, human smuggling, prevent natural disasters and protect the environment."
Among the humanitarian issues pending between the two countries is the continued imprisonment of American Alan Gross, who the Cuban government accuses of illegally bringing communications equipment onto the island while on a USAID-funded democracy building programme. In March of this year he was sentenced to 15 years in prison for crimes against the state.
Cuban officials including President Raul Castro accused him of spying, but Mr Gross says he was only trying to help the island's tiny Jewish community get internet access.
The case has harmed any chance of improved relations between Washington and Havana, which briefly seemed to be getting better after Mr Obama assumed the presidency.
In an interview with The New York Times during his current visit to the United States, Mr Rodriguez did not rule out the possibility of Mr Gross being freed for humanitarian reasons, but indicated Cuba would expect some kind of reciprocal action.