NEW YORK, Sept 22 (Reuters) - U.S. President Donald Trump attacked Venezuela's authoritarian government from the podium at the United Nations this week but Latin American leaders say that behind the scenes he listened to them on how best to resolve the delicate regional crisis.
Latin American leaders who dined with Trump on Monday on the fringes of the U.N. General Assembly said they told him that a military invasion, a threat he casually made last month, would be unacceptable in a region long-sensitive to heavy-handed intervention by Washington.
They pressed on him the need for a peaceful transition to democracy in Venezuela and argued against economic sanctions that would deepen its humanitarian crisis, which has already sent tens of thousands fleeing to neighboring countries.
"Trump went to the trouble of asking us how best to solve the Venezuelan situation," Argentine Foreign Minister Jorge Faurie, who attended the dinner, told Reuters. "That the United States would consult Latin American counties on what to do is in itself a major step forward."
At the United Nations General Assembly this week, Trump attacked the Socialist government of President Nicolas Maduro for destroying a once-wealthy oil-producing nation. He threatened to increase sanctions if Maduro did not move toward restoring democratic rule.
But Trump steered clear of repeating the threat of military action he made on Aug. 11 which alarmed Latin Americans. For many, it conjured memories of the 1989 U.S. invasion of Panama that overthrew dictator Manuel Noriega, who died in May after years in prison in the United States and his own country.
At least 125 people were killed in Venezuela during four months of protests this year against Maduro, who has resisted calls to bring forward a presidential election and instead set up a legislative superbody to overrule the opposition-led Congress.
While no decisions were taken, the talks between Trump and the presidents of Brazil, Colombia and Panama, and the vice president of Argentina put pressure on Maduro to engage in real negotiations with his opponents instead of using talks to gain time, Latin American leaders said.
Brazilian President Michel Temer told reporters after the dinner those present had agreed to ramp up pressure on Venezuela without direct intervention.
President Juan Carlos Varela of Panama said the dinner with Trump strengthened an initiative by a dozen Latin American countries and Canada to back a new round of negotiations between Maduro and his opponents.
"There will be more pressure to convince Maduro to accept free and democratic elections in 2018," Varela told Reuters. "We think Maduro is getting the message that change must come."
Purchases of crude and refined products from Venezuela represented 7 percent of total U.S. oil imports in the first half of the year, giving Washington some leverage to push for political change in the South American nation.
Yet an oil embargo - which would deprive the Maduro government of its main source of income - was not discussed at the dinner with Trump, several attendees said.
Much of Venezuelan oil is heavy in sulfur and used for heating oil and asphalt, but is also refined into gasoline, mainly by U.S. Gulf refiners. Gulf state senators have urged Trump not to ban imports, which would hurt refineries and push up gasoline prices.
Colombian foreign minister María Angela Holguin said an oil boycott would only extend the suffering of the Venezuelan people, who are facing shortages of food and medicine.
"We have to think of the Venezuelans who would suffer even more if the economic crisis deepens," she said.
Formal negotiations with the opposition are due to begin in the Dominican capital of Santo Domingo on Sept. 27 and involve observers from Mexico, Chile, Nicaragua and Bolivia.
Argentina's Faurie said the Maduro government would have to agree to several conditions for talks to be taken seriously, including a calendar for elections monitored by international observers and the release of political prisoners.
Eric Farnsworth, vice president of the Americas Society, a business forum dedicated to fostering ties between the United States and Latin America, said the talks between Trump and regional leaders sent a clear message to Maduro.
"The most important thing that came out of the dinner was the photograph showing the president and the vice president of the United States sitting down with regional leaders to talk about Venezuela," Farnsworth said. (Reporting by Anthony Boadle; Additional reporting by Mariana Párraga in Houston; Editing by Daniel Flynn and Andrea Ricci)