The meeting on the sidelines of the Summit of the Americas was an important step for Mr. Obama as he seeks to ease tensions with Cuba and defuse a generations-old dispute that has also affected relations with the other countries of the region.

Since his first foray to the summit meeting three months after taking office, Mr. Obama has seen one bone of contention frustrate his efforts to reach out to the United States’ hemispheric neighbors: the fact that Cuba was blackballed from the gathering. He was scolded by Argentina’s president for maintaining an “anachronistic blockade,” lectured by Bolivia’s president about behaving “like a dictatorship,” and in 2012 blamed for the failure of leaders to agree on a joint declaration — the result, his Colombian host said, of the dispute over Cuba.

This year, Mr. Obama came to the summit meeting here determined to change the dynamic with a series of overtures to Cuba. In addition to the meeting with Mr. Castro, 83, the gathering was the first time in the more than 20-year history of the summit meeting that Cuba was allowed to attend.

“The United States will not be imprisoned by the past — we’re looking to the future,” Mr. Obama, 53, said of his approach to Cuba at the summit meeting’s first plenary session on Saturday. “I’m not interested in having battles that frankly started before I was born.”

“The Cold War,” he added, “has been over for a long time.”

He said the shift in policy would be a turning point for the entire region. Mr. Castro, in a speech of more than 45 minutes that went well beyond the allotted eight minutes, spoke in unusually warm tones about an American president who has sought reconciliation with his country. But in a nod to allies like Venezuela that still support Cuba, he also delivered a lengthy diatribe on historical American injustices in the hemisphere.

Mr. Castro said he had read Mr. Obama’s books and praised his background as “humble.” He saluted his “brave” decision to take steps against a trade embargo against Cuba by using his executive powers to loosen a host of travel and commerce restrictions. And he thanked Mr. Obama for vowing a “rapid decision” on removing Cuba from the United States government’s list of states that sponsor international terrorism, a designation that has hobbled Cuba’s ability to bank with the United States and some foreign creditors.