US President Barack Obama met Cuban President Raul Castro yesterday in the highest-level talks between the two countries in nearly 60 years, and the two men agreed to push ahead on improving relations after decades of hostility.

Describing their private meeting as “historic,” Obama said the two countries can now end the antagonism of the Cold War era, although he said he would continue to pressure the communist-led country on democracy and human rights.

“Obviously there are still going to be deep and significant differences between our two governments,” Obama told Castro as they met in Panama, where they both attended a summit of leaders from across the Americas.

The US President said he believed both sides could raise their concerns about the other’s policies yet still work together to boost commercial, travel and diplomatic ties.

“The Cold War is over ... Cuba is not a threat to the United States,” Obama later told reporters, pointing out that at 53, he wasn’t even born when Castro and his brother Fidel seized power in the 1959 Cuban revolution. The meeting followed a landmark agreement in December, when Obama and Castro announced they would move to normalise relations, including seeking to restore diplomatic ties that were broken off by Washington in 1961.

Obama said he decided to overturn longstanding US policy on Cuba because the old approach of open hostility and economic sanctions had failed to force through major changes on the Caribbean island and it was time to try something new.

Since then, he has relaxed some restrictions on travel and trade with Cuba, although a longstanding economic embargo remains in place.

Some things we will agree on, others we will disagree

At their 80-minute meeting, almost unimaginable until recently, Obama and Castro sat side by side in polished, wooden chairs in a small conference room. The mood was described by Obama aides as cordial but businesslike. Both men nodded and smiled as the other spoke. Castro said he would continue to take steps toward normalising relations, and was open to discussing human rights and other issues.

“So we are willing to discuss everything, but we need to be patient, very patient. Some things we will agree on; others we will disagree,” said the 83-year-old leader, who took over as president of Cuba in 2008 when Fidel Castro stepped aside because of ill health.

During a summit session earlier, Castro apologised to Obama for a series of impassioned broadsides against the US for its Cold War attempts to topple communist rule on the island.

He said the US leader was not to blame for any of those policies of the past.

Castro has already undertaken some market-style reforms to try to strengthen Cuba’s economy but he is moving cautiously and he has made clear that he has no intention of allowing an end to communist rule.

Obama, a Democrat, has faced some criticism inside the US Congress for his dramatic shift on Cuba policy. Critics say he has given up too much without first insisting on political reform on the island.

The last time the leaders of the two countries held a substantive meeting was in 1956, when Dwight Eisenhower was US president and Fulgencio Batista was the US-backed dictator in power in Havana.

The Castro brothers toppled Batista in a revolution on January 1, 1959 and relations between the US and Cuba quickly deteriorated.

Fidel Castro became a Cold War ally of the Soviet Union and the rivalries took the world to the brink of a nuclear war in the Cuban Missile Crisis of October, 1962.