Shortages of food and medicine have left Peru calling for a bloc of countries to pressure Mr. Maduro to accept humanitarian donations, something that he declines to do. Mercosur, the South American trade bloc, has threatened to expel Venezuela over human rights violations and not complying with its trade laws.

And even the State Department, after Mr. Kerry’s meeting with Mr. Maduro, issued a statement indicating that the men’s encounter in Cartagena was not a photo op but rather Mr. Kerry’s chance to express “our concern about the economic and political challenges that have affected millions of Venezuelans.”

The year, marked by economic collapse, has been one of the most unstable for Venezuela, leading to fears among diplomats who now struggle for ways to reach out to a country whose leftist leaders have closed ranks.

Triple-digit inflation and a 10 percent economic contraction are expected this year at the same time that Mr. Maduro has faced a congress led by the opposition and a growing movement to oust him. But Mr. Maduro has doubled down, surrounded himself with a cadre of hard-liners and military men, blocked the congress with his courts and locked up many people who demand a recall vote.