He described the meeting on the fringes of the Summit of the Americas as “candid and fruitful”.
Mr Obama said that the former foes would continue to have differences but that they could advance their mutual interests.
The meeting was the first formal talk between the two countries’ leaders in half a century.
“What we have both concluded is that we can disagree with a spirit of respect and civility,” said President Obama. “Over time, it is possible for us to turn the page and develop a new relationship between our two countries.”
His remarks came at the end of a regional summit which has been dominated by the historic thaw between US-Cuba relations.
Cuban leader Raul Castro said that the two countries had “agreed to disagree” when necessary.
“We are disposed to talk about everything, with patience,” he said. “Some things we will agree with, and others we won’t.”
Earlier, the Cuban leader referred to Obama as an “honest man” after a lengthy speech largely taken up with the history of the relationship between the US and Cuba.
“When I talk about the revolution, the passion oozes out of me,” the Cuban leader said. “I have to ask President Obama for forgiveness. He is not responsible for the things which happened before his time.”
Latin American and Caribbean leaders at the summit in Panama have welcomed the reconciliation.
Brazilian President Dilma Rousseff hailed it as a courageous effort to end the last vestiges of the Cold War, which she said had caused great damage in the hemisphere.
President Cristina Fernandez de Kirchner of Argentina gave the main credit to Cuba, saying it had fought with unprecedented dignity against the US blockade. (BBC)