Not satisfied with just one tweet, Mr. Rubio followed up with four more on the topic on Monday and even more on Tuesday. In one of the tweets on Monday, he shared the phone number for the chef’s steakhouse in Miami, one of two locations in the United States, “in case anyone wanted to call,” said Mr. Rubio, whose state has the largest Venezuelan-American population in the country.

Before long, the videos had been deleted. In the clips preserved by The Herald, Mr. Gokce grips the meat and the knife while wearing black disposable gloves. Mr. Maduro, puffing on a cigar, smiles and laughs. Later, the president admires a shirt the chef presents him. And before Mr. Maduro and his wife, Cilia Flores, leave the restaurant, the chef and the president embrace in a hug.

The rack of lamb, which Mr. Gokce cut into individual chops, costs $250 at his restaurant in Manhattan. Meanwhile in Venezuela, food prices have skyrocketed to the point where people go without meals and two-thirds of hospitals said in 2016 that they did not have any infant formula for babies.

The virtual uproar seemed to encapsulate something about this bizarre era’s intersection of politics and pop culture. An over-the-top celebrity chef made famous by Instagram had inadvertently exposed the high life of a leader regarded as a despot by his neighbors.

Mr. Maduro already had a reputation as an infamous glutton indifferent to hunger in his country, having once been caught sneaking bits of an empanada while giving a live address on TV.

And then there was the senator, a failed candidate for president of a country that once considered supporting a coup in Venezuela, adopting a tactic used by President Trump, the man who defeated him in the Republican primaries: using Twitter to put his target on blast.