Venezuelan opposition leader Juan Guaidó holds a press conference in Caracas in early May, calling for peaceful demonstrations days after an uprising to oust President Nicolás Maduro. (Eva Marie Uzcategui/Getty Images)

When Vice President Pence delivered an applause line on Venezuela to an audience of Latin American business leaders and government officials this week, the silence was deafening.

“I came today to be very clear,” Pence said in a speech to the Americas Society/Council of the Americas. The United States was using diplomatic and economic pressure against the Maduro regime, he said, and then paused for emphasis.

“But to those who continue to oppress the good people of Venezuela, know this: All options ARE on the table.”

Latin Americans, who already see the Venezuelan crisis spilling over their borders in the form of millions of refugees, appreciate U.S. interest and determination. The threat of U.S. military intervention, not so much.

The history of U.S. invasion and occupation in the region, along with covert involvement in regime change, is long and troubled. Mexico, Guatemala, Nicaragua, Haiti, Cuba, Chile, and more. Even those leaders who might be happy to see Venezuelan President Nicolás Maduro ousted with U.S. force believe there would be a heavy price to pay among their own constituents.

As U.S. threats toward Venezuela and Cuba, one of Maduro’s primary backers, have grown more explicit in recent days, Latin American and European governments have nervously stepped up their efforts toward a political solution. All back the opposition led by Juan Guaidó, the self-declared president of an interim government trying to take over, as does the United States.

“Up to now, although their rhetoric is a bit different, the United States and the members of the Lima Group converge,” said a senior Latin American diplomat, referring to the coalition of 14 Latin countries and Canada that has also called for Maduro to leave.

“The only possibility that could impact that is the possibility of military intervention,” said the diplomat, who represents one of the Lima Group countries and spoke on the condition of anonymity to talk frankly about a feeling other countries largely share.

Some Latin American officials believe that the Trump administration — and a president known to dislike overseas wars — is talking about intervention mostly to keep the pressure on Maduro.

One official compared it to psychological operations, a conflict being fought only “in social media, newspapers, television, etc.”

“There is a lot being said here, messages being sent from side to side. . . . The temperature being kept up. If you don’t pressure Mr. Maduro, he will be very comfortable where he is sitting,” the official said.

But, the official said, he did not believe the United States was genuinely close to taking military action. “It’s not in our cards — not in the cards of the Lima Group. I don’t think it’s happening.”

As the administration tends to do, Pence attributed democratic elections across Latin America since Trump came to power two years ago to the president’s own intervention, despite the wave of democratization that began in the late 1970s. Quoting Trump, he cited “a new day . . . coming in Latin America,” where “socialism is dying, and liberty, prosperity and democracy are being reborn.”

The only thing standing in the way, the administration has argued, is socialism in Venezuela, Cuba and Nicaragua.

Some regional experts have argued that Trump’s immigration policies, his slashing of democracy aid to the region, and his general lack of interest have instead promoted a lean toward authoritarianism. Trump was the first American leader not to ­attend the Summit of the Americas, sending Pence instead, and has visited the region only once, when last year’s Group of 20 conference was held in Argentina.

In its most recent communique, last Friday, the Lima Group emphasized its commitment to a peaceful resolution of the Venezuela crisis, and called for wider consultations within the inter­national community — including reaching out to the European-led International Contact Group, and to Cuba.

The Contact Group, which includes eight leading European countries and the European Union, as well as Costa Rica, Ecuador and Uruguay, has not demanded Maduro’s departure from Venezuela — as have the Lima Group and Trump — but instead has called for a political solution and early elections under an international umbrella.

“Our goals are the same, which are to provide a platform for change of government in Venezuela,” the senior Latin American diplomat said of the two groups. At their last meeting, the diplomat said, “we decided to reach out to every single stockholder.”

“Countries were assigned to take a role and reach out — to Russia, to Cuba, to the Contact Group.” Immediately after release of the latest Lima communique, Canadian Prime Minister Justin Trudeau telephoned Cuban President Miguel Díaz-Canel. The next day, European Union foreign policy chief Federica Mogherini, on behalf of the Contact Group, spoke with Cuban Foreign Minister Bruno Rodríguez.

The administration has stressed that its policies have wide support in the hemisphere, and that Cuba must be shunned and punished for its support of Maduro. It has rejected Cuban and Russian calls for dialogue as ploys to gain time for Maduro.

But despite being an influential player from the sidelines, the United States does not belong to either the Lima or Contact groups, and there is a sense that its putative allies are moving away from the administration’s escalating saber-rattling.

“Our own position has to be clear,” the diplomat said. “We do not support international [military] intervention.”

Some members of the Lima Group have also expressed a willingness to proceed with a political solution even if it doesn’t mean Maduro’s immediate departure. “It would depend on the timetable,” said the diplomat, referring to some kind of “interim period,” in which Maduro would step down from the presidency, while the electoral process was underway.

Mogherini also said that the European-led group had drawn up a list of “options” to resolve the crisis, and would send a high-level political delegation to Caracas to explore them with both sides.

“We’ve been very clear from the beginning,” Mogherini said, “that we believe there should be no military attempts, from within or outside the country, to solve the crisis through military means or the use of force in any form.”

Not every member was pleased with last week’s Lima declaration.

Colombian Vice President Marta Lucía Ramírez, who is in Washington for meetings with the Trump administration, expressed consternation at the outreach to Cuba.

“We all want a peaceful transition” in Venezuela, Ramírez said. But “we have to use all methods so Maduro departs.” She called for increased sanctions on those around him.

The ongoing crisis has placed a severe strain on Colombia, which has taken in nearly 2 million Venezuelan refugees. “We are reaching our limit,” she said. If “we give any oxygen” to Maduro and those around him, “it is just going to prolong” the situation.

But Colombia is also opposed to military intervention. “I cannot influence the discussion” in Washington, she said, but “we are not discussing [military intervention] in Colombia.”

Anthony Faiola in Caracas contributed to this report.