PORT OF SPAIN, Trinidad and Tobago — President Obama, seeking to thaw long-frozen relations with Cuba, told a gathering of Western Hemisphere leaders on Friday that “the United States seeks a new beginning with Cuba,” and that he was willing to have his administration engage the Castro government on a wide array of issues.

Mr. Obama’s remarks, during the opening ceremony at the Summit of the Americas, are the clearest signal in decades that the United States is willing to change direction in its dealings with Cuba. They capped a dizzying series of developments this week, including surprisingly warm words between Raúl Castro, Cuba’s leader, and Secretary of State Hillary Rodham Clinton.

Other leaders here said that in watching Mr. Obama extend his hand to Cuba, they felt they were witnessing a historic shift. And in another twist, Cuba’s strongest ally at the summit, President Hugo Chávez of Venezuela, no fan of the United States, was photographed at the meeting giving Mr. Obama a hearty handclasp and a broad smile.

Cuba is not on the official agenda here; indeed, Cuba, which has been barred from the Organization of American States since 1962, is not even on the guest list. But leaders in the hemisphere have spent months planning to make Cuba an issue here.

The White House was well aware that if Mr. Obama did not address it head on, the issue would overwhelm the rest of the summit gathering. This week, the president opened the door to the discussions by abandoning longstanding restrictions on the ability of Cuban-Americans to travel freely to the island and send money to relatives there.

“I know there is a longer journey that must be traveled in overcoming decades of mistrust, but there are critical steps we can take toward a new day,” Mr. Obama said, adding that he was “prepared to have my administration engage with the Cuban government on a wide range of issues — from human rights, free speech, and democratic reform to drugs, migration, and economic issues.”

Mr. Obama’s message was not entirely new; he has said in the past that he was willing to engage with Cuba. But making a public pledge before leaders of 33 other nations, many of whom he had not yet met, gave his words added heft.

He came here with the aim of reaching out to leaders in a region that felt ignored by the United States during the Bush years. Just as he campaigned on the theme of change when running for the White House, he made change a theme of his speech here, saying: “I didn’t come here to debate the past. I came here to deal with the future.”

He said the United States needed to acknowledge long-held suspicions that it has interfered in the affairs of other countries. But, departing from his prepared text, he also said the region’s countries needed to cease their own historic demonization of the United States for everything from economic crises to drug violence.

“That also means we can’t blame the United States for every problem that arises in the hemisphere,” he said. “That’s part of the bargain. That’s the old way, and we need a new way.”

On Cuba, the president’s words were as notable for what he said as for what he did not say. He did not scold or berate the Cuban government for holding political prisoners, as his predecessor, George W. Bush, often did.

But he also did not say that he was willing to support Cuba’s membership in the Organization of American States, or lift the 47-year-old trade embargo against Cuba, as some hemisphere leaders here want him to do.

And his press secretary, Robert Gibbs, speaking to reporters aboard Air Force One on the way here, pointed out that Cuba needed to take concrete action to “bring greater freedom to the Cuban people.”

In his speech, Mr. Obama gave a nod toward these issues, although not explicitly.

“Let me be clear,” he said. “I am not interested in talking for the sake of talking. But I do believe we can move U.S.-Cuban relations in a new direction.”

The new tone from Washington drew warm praise from leaders like President Cristina Fernández de Kirchner of Argentina and President Daniel Ortega of Nicaragua. Mr. Ortega, who said he felt ashamed that he was participating in the summit meeting without the presence of Cuba, evoked images of the collapse of the Berlin Wall, saying, “I am convinced that wall will collapse, will come down.”

Mrs. Kirchner praised Mr. Obama for “what you did to stabilize the relationship from the absurd restrictions imposed by the Bush administration,” adding: “We sincerely believe that we in the Americas have a second opportunity to construct a new relationship. Don’t let it slip away.”

Mr. Obama’s speech on Friday night was only the latest in a string of overtures between the countries. On Thursday, Raúl Castro, Cuba’s president, used unusually conciliatory language in describing the Obama administration’s decision to lift restrictions on family travel and remittances.

“We are willing to discuss everything, human rights, freedom of press, political prisoners, everything, everything, everything they want to talk about, but as equals, without the smallest shadow cast on our sovereignty, and without the slightest violation of the Cuban people’s right to self-determination,” Mr. Castro said in Venezuela during a meeting of leftist governments meant as a counterpoint to this weekend’s summit meeting in Trinidad and Tobago.

On Friday, Mrs. Clinton responded, saying, “We welcome his comments, the overture that they represent, and we’re taking a very serious look at how we intend to respond.”

Earlier this week Brazilian officials signaled in Rio de Janeiro that President Luiz Inácio Lula da Silva, potentially flanked by the Colombian president, Álvaro Uribe, would raise the issue of accepting Cuba into the Organization of American States at the summit meeting. Cuba’s “absence is an anomaly and he is waiting for this situation to be corrected,” Marco Aurélio García, Mr. da Silva’s foreign policy adviser, told reporters.

On Friday, the secretary general of the O.A.S., José Miguel Insulza, said he would call for Cuba to be readmitted. And Mr. Chávez recently said he would refuse to sign the official declaration produced at the summit meeting because Cuba was not invited.

There are no plans for Mr. Chávez and Mr. Obama to meet privately, but White House officials said before the meeting that the two would participate in at least one small group leaders’ meeting, and that Mr. Obama would not spurn any outreach by Mr. Chávez, who frequently referred to Mr. Bush as “the devil.”

Indeed, Mr. Obama made the first move, officials said, striding across the room to introduce himself to Mr. Chávez as the leaders were lining up to parade into the opening ceremony. As he extended his hand, the Venezuelan government reported, Mr. Chávez told Mr. Obama: “I greeted Bush with this hand eight years ago. I want to be your friend.”