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“The specter of Iran raises red flags in a way that China doesn’t, because China tends to respect the American sphere of influence,” said Julia E. Sweig, a Latin American expert at the Council on Foreign Relations.

Iran’s motives are murkier, according to administration officials. It has cultivated wide-ranging economic ties with Venezuela and, to a lesser extent, Nicaragua. But it has also been linked to the bombing of a Jewish community center in Buenos Aires in 1994, which killed 85 people.

Iran is not known to have a big presence in El Salvador, officials said, and it was not represented at Mr. Funes’s inauguration. But the change in power after 17 years of a pro-American right-wing government could offer an opening.

Senator John Ensign, Republican of Nevada, said on CNN that it was “irresponsible for the president” to be seen laughing and joking with “one of the most anti-American leaders in the entire world,” referring to Mr. Chávez.And Senator Lindsey Graham, Republican of South Carolina, pointed to Cuba’s estimated 200 political prisoners. “Release the prisoners and we’ll talk to you,” he said of the Cuban government on Fox News Sunday, adding, “Put up or shut up.”

Mr. Obama defended his overtures at a news conference on Sunday, saying the handshakes and the polite conversation he shared with Mr. Chávez here were hardly “endangering the strategic interests of the United States.”Wrapping up a four-day swing through Latin America, he said he believed he had paved the way for “frank dialogue” with countries like Venezuela and Cuba, whose relations with the United States have been badly strained.But he also sought to calibrate his message, saying Sunday that he had “great differences” with Mr. Chávez and insisting that freedom for the Cuban people would remain the guiding principle of his foreign policy.

Despite the warm feelings, some old tensions remained. President Evo Morales of Bolivia confronted Mr. Obama during a private session on Saturday with a charge that the United States had plotted to assassinate him. Mr. Obama responded on Sunday, saying, “I am absolutely opposed and condemn any efforts at violent overthrows of democratically elected governments.”

And President Daniel Ortega of Nicaragua, an old Washington nemesis, sought to embarrass Mr. Obama in a nearly one-hour speech filled with anti-American vitriol in which he likened the American embargo of Cuba to the Berlin Wall.

Hoping to push the process forward, leaders from Latin America and the Caribbean have volunteered to aid in a reconciliation between the United States and Cuba. “Brazil would be able to help,” Mr. da Silva said Sunday. In an interview published Sunday in the Spanish newspaper ABC, he said the United States should not wait for Cuba to take the next step in efforts to end their half-century of feuding.

Mr. Chávez took the initiative Saturday, saying he was naming Roy Chaderton, Venezuela’s representative to the Organization of American States, to be his new ambassador to Washington.

Mr. Chávez had ejected the American ambassador to Venezuela in September, saying he had discovered an American-backed plot to remove him from power. Washington responded in kind.

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.”

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.

“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.