Cuban President Raul Castro and US leader Barack Obama prodded each other over human rights and the long-standing US economic embargo, even as the two men pledged to set aside their decades-long differences and move forward with normalising ties.

Following a historic meeting in Havana on Monday, Obama welcomed what he called a "new day" in relations between the two countries, but repeatedly pushed Castro to take steps to address Cuba's human rights record.

"America believes in democracy. We believe that freedom of speech and freedom of assembly and freedom of religion are not just American values but are universal values," Obama said, standing alongside Castro after their meeting at Havana's Palace of the Revolution.

Yet, Castro, who took the rare step of taking questions from journalists, hit back at what he called US "double standards", saying Cuba found it "inconceivable" for a government to fail to ensure healthcare, education, food and social security for its people - a clear reference to the US.

"We defend human rights," Castro said. "In our view, civil, political, economic, social and cultural rights are indivisible, interdependent and universal."

When asked about political prisoners in Cuba, Castro pushed back aggressively, saying if the journalist could offer names of anyone improperly imprisoned, "they will be released before tonight ends".

"Give me a list of the political prisoners and I will release them immediately. Just mention the list. What political prisoners?" said Castro.

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The Cuban leader praised Obama's recent steps to relax controls on his country as "positive", but deemed them insufficient. He called anew for the US to return its naval base at Guantanamo Bay to Cuba and to lift the US trade embargo.

"That is essential, because the blockade remains in place, and it contains discouraging elements," Castro said.

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The main sticking point for bilateral relations is the devastating trade embargo imposed on Havana in 1962 by former US President John F Kennedy.

In the same year, the movement of nuclear missiles from the Soviet Union to Cuba brought the countries close to nuclear war.

"The embargo is going to end - exactly when I can't be sure," Obama told the news conference, noting it was up to the US Congress to finish it.

Obama came to Cuba pledging to press its leaders on human rights and political freedoms, and vowing that the mere fact of a visit by an American leader would promote those values on the island.

He responded to Castro's remarks about the human rights of the US by saying that his country should not be immune or afraid of criticism, and he welcomed the Cuban leader's comments on areas where the United States is "falling short".

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Obama said he had raised "very serious differences" the US has with Cuba on democracy and human rights, but portrayed those difficult conversations as a prerequisite to closer relations.

Crediting Cuba for making progress as a nation, Obama said part of normalising relations between the two countries means "we discuss these differences directly".

"The future of Cuba will be decided by Cubans - not by anybody else," Obama said. "At the same time, as we do wherever we go around the world, I made it clear the US will continue to speak up about democracy, including the right of the Cuban people to decide their own future."

As Castro prepares to step down in 2018, he has held firm against any changes to Cuba's one-party political system.

Cubans expressed shock at seeing Castro answer questions from reporters live on state TV.

"It's very significant to hear this from our president, for him to recognise that not all human rights are respected in Cuba," Raul Rios, a 47-year-old driver, told the AP news agency.

Rios said he agreed with Castro's argument that no country is perfect and all should strive to do better.

Marlene Pino, 47, an engineer, said: "This is pure history and I never thought I'd see something like this. It's difficult to quickly assimilate what's happening here. For me it's extraordinary to see this."