Cuban President Raul Castro and US President Barack Obama sparred over human rights issues including the American prison at Guantanamo Bay and Cuba’s political prisoners, the BBC reports.
At a historic news conference, Mr Castro said if he was given a list of political prisoners, he would “release them tonight”.
The White House has said it has given Cuba lists of dissidents in the past.
Mr Castro does not view the prisoners as dissidents, US officials said.
That disagreement is central to the conflict between US and Cuban officials.
More needs to be done to lift the US embargo on trade with Cuba, Mr Castro said, adding that the Guantanamo Bay detention camp must close.
Mr Obama, the first serving US president to visit Cuba since 1959, said the trade embargo would be fully lifted.