PANAMA CITY - President Barack Obama and Cuba's Raul Castro sat down together Saturday in the first formal meeting of the two country's leaders in a half-century, pledging to reach for the kind of peaceful relationship that has eluded their nations for generations.

In a small conference room in a Panama City convention center, the two sat side by side in a bid to inject fresh momentum into their months-old effort to restore diplomatic ties. Reflecting on the historic nature of the meeting, Obama said he felt it was time to try something new and to engage with both Cuba's government and its people.

"What we have both concluded is that we can disagree with a spirit of respect and civility," Obama said. "And over time, it is possible for us to turn the page and develop a new relationship between our two countries."

Castro, for his part, said he agreed with everything Obama had said - a stunning statement in and of itself for the Cuban leader. But he added the caveat that they had "agreed to disagee" at times. Castro said he had told the Americans that Cuba was willing to discuss issues such as human rights and freedom of the press, maintaining that "everything can be on the table."

"We are disposed to talk about everything - with patience," Castro said in Spanish. "Some things we will agree with, and others we won't."

Not since 1958 have a U.S. and Cuban leader convened a substantial meeting; at the time, Dwight Eisenhower was in the White House and Fulgencio Batista in charge in Cuba. But relations quickly entered into a deep freeze amid the Cold War, and the U.S. spent decades trying to either isolate or actively overthrow the Cuban government.

In a stroke of coincidence, Eisenhower's meeting with Batista in 1958 also took place in Panama, imbuing Saturday's session between Obama and Castro with a sense of having come full circle.

The historic gathering played out on the sidelines of the Summit of the Americas, which this year included Cuba for the first time. Although the meeting wasn't publicly announced in advance, White House aides had suggested the two leaders were looking for an opportunity to meet while in Panama and to discuss the ongoing efforts to open embassies in Havana and Washington, among other issues.

At the start of their hour-long meeting, Obama acknowledged that Cuba, too, would continue raising concerns about U.S. policies - earning a friendly smirk from Castro. Obama described the sit-down later as "candid and fruitful" and said he and Castro were able to speak about their differences in a productive way.

Even still, raw passions were on vivid display earlier in the day when Castro, in a meandering, nearly hour-long speech to the summit, ran through an exhaustive history of perceived Cuban grievances against the U.S. dating back more than a century.

Then, in an abrupt about face, he apologized for letting his emotions get the best of him. He said many U.S. presidents were at fault for that troubled history - but that Obama isn't one of them.

"I have told President Obama that I get very emotional talking about the revolution," Castro said through a translator, noting that Obama wasn't even born when the U.S. began sanctioning the island nation. "I apologize to him because President Obama had no responsibility for this."

Obama agreed.

"The Cold War has been over for a long time," he said. "And I'm not interested in having battles frankly that started before I was born."

The flurry of diplomacy kicked off Wednesday when Obama and Castro spoke by phone - only the second known call between U.S. and Cuban presidents in decades. It continued Friday evening when Obama and Castro traded handshakes and small talk at the summit's opening ceremonies, setting social media abuzz with photos and cellphone video.

Obama and Castro sent shockwaves throughout the hemisphere in December when they announced the plan for rapprochement, and their envoys have spent the ensuing months working through thorny issues such as sanctions, the re-opening of embassies and the island nation's place on the U.S. list of state sponsors of terrorism.

Although earlier in the week Obama suggested a decision to remove Cuba from the list was imminent, he declined to take that step Saturday, citing the need to study a recently completed State Department review. Lawmakers briefed on that review have said it resulted in a recommendation that Cuba be delisted.

Removal from the terror list is a top priority for Castro because it would not only purge a stain on Cuba's pride, but also ease its ability to conduct simple financial transactions.