President Barack Obama and his Cuban counterpart Raul Castro have held a historic joint news conference in Havana, discussing human rights and lifting the trade embargo.

Both presidents agreed to work together, despite wrangling over human rights.

Raul Castro said more needed to be done to lift the US embargo on trade with Cuba and that the Guantanamo Bay detention camp must close.

Barack Obama, the first sitting US president to visit Cuba since 1959, said the trade embargo would be fully lifted.

Raul Castro took questions from reporters – a rarity for him.

“Cuba’s destiny will not be decided by the United States or any other nation… The future of Cuba will be decided by Cubans not by anybody else,” Barack Obama said.

Asked about political prisoners in Cuba, Raul Castro denied it, telling journalists to “give him a list” and then they would be released “tonight”.

The Cuban president also defended his country’s record on human rights and pointed to problems in the US.

“We defend human rights, in our view civil, political, economic, social and cultural rights are indivisible, inter-dependent and universal,” Raul Castro said.

Raul Castro is not usually subject to any aggressive questioning from reporters and called the prisoners question “not polite”, later ending the news conference by saying: “I think this is enough.”

“Actually we find it inconceivable that a government does not defend and ensure the right to healthcare, education, social security, food provision and development,” he said.

Barack Obama could not say exactly when the trade embargo would be lifted, but recognized it was necessary.

“The reason is what we did for 50 years did not serve our interests or the interests of the Cuban people,” he said.

His administration has done what it can on lifting trade restrictions, Barack Obama said, but further action will require Congress which is “not as productive in an election year”.

Barack Obama also said further easing of the trade embargo will depend on actions Cuba takes on human rights.

He said it is not just Cuba that the US has “deep disagreements” about human rights with – it also has disagreements with China and Vietnam.

“I believe if I engage frankly, clearly, stating our beliefs but I can’t force change on any country – it ultimately has to come from within – that is a more useful strategy,” he said.

“I have faith in people.”

Reporters described the press conference as “tense” and “remarkable”.

Before the speech, it was announced that Google was opening an online technology center for free Internet access at much higher speeds than what is available in Cuba now.

Google hopes the center will be part of a larger effort to improve Internet access in Cuba.