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 US 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 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 US trade embargo on Cuba.