Port-of-Spain, Trinidad ? Defending his brand of world politics, President Barack Obama said Sunday that he “strengthens our hand” by reaching out to enemies of the United States and making sure that the nation is a leader, not a lecturer, of democracy.

Obama’s foreign doctrine emerged across his four-day trip to Latin America, his first extended venture to a region of the world where resentment of U.S. power still lingers. He got a smile, handshakes and even a gift from incendiary leftist leader Hugo Chavez of Venezuela, and embraced overtures of new relations from isolated Cuban President Raul Castro.

“The whole notion was that if we showed courtesy or opened up dialogue with governments that had previously been hostile to us, that that somehow would be a sign of weakness,” Obama said, recalling his race for the White House and challenging his critics today.

“The American people didn’t buy it,” Obama said. “And there’s a good reason the American people didn’t buy it — because it doesn’t make sense.”

Still, Obama made sure to inject some go-it-slow caution and clear expectations for U.S. foes as he capped his trip to twin-island nation of Trinidad and Tobago with a steamy outdoor news conference.

On Cuba, he said Castro should release political prisoners, embrace democratic freedoms and cut fees on the money that Cuban-Americans send back to their families. Obama has lifted some restrictions on Cuba, and Castro responded with a broad, conciliatory overture.

“The fact that you had Raul Castro say he’s willing to have his government discuss with ours not just issues of lifting the embargo, but issues of human rights, political prisoners, that’s a sign of progress,” Obama said. “And so we’re going to explore and see if we can make some further steps.”

He did not, though, offer any sign of lifting the crushing U.S. trade embargo on Cuba, as many Latin American and U.S. leaders want. Obama acknowledged that the U.S. policy in Cuba for the last 50 years “hasn’t worked” but said change will be gradual.

In Washington, both Democrats and Republicans said Sunday that they wanted to see actions, not just rhetoric, from Cuba.

“Release the prisoners and we’ll talk to you. … Put up or shut up,” said Sen. Lindsey Graham, R-S.C.

“I think we’re taking the right steps, and I think the ball is now clearly in Cuba’s court,” said Sen. Claire McCaskill, D-Mo. “They need to respond and say what they’re willing to do.”

Obama returned to Washington early Sunday evening. But even before he got back, Obama was facing condemnation from some Republicans about how he dealt with Chavez. “I think it was irresponsible for the president to be seen kind of laughing and joking with Hugo Chavez,” said Sen. John Ensign, R-Nev.

The president brushed that aside, noting that Venezuela has a defense budget about one-six hundredth the size of the United States’ and owns the oil company Citgo.

“It’s unlikely that as a consequence of me shaking hands or having a polite conversation with Mr. Chavez that we are endangering the strategic interests of the United States,” Obama said.