By Alexandra Ulmer

RIO DE JANEIRO (Reuters) - When Venezuelan fencer and former sports minister Alejandra Benitez was eliminated in her second-round bout at the Rio Games, she wore a uniform emblazoned with the eyes of the country's divisive late leader, Hugo Chavez.

Back home, it was too much for TV viewers who blame Chavez and his followers for a collapsed economy, and they went online to say the revolutionary's eyes had brought her bad luck.

Benitez, 36, promptly hit back in a video, this time donning a t-shirt with a stylized drawing of the leftist politician's eyes over the Olympic rings: "Look at the beautiful eyes of my 'Comandante', so that it hurts you even more," she said.

The acrimonious politics of Venezuela had arrived in Rio.

Once booming from oil with a growing middle class, the country is in crisis: food is so scarce that mobs riot outside supermarkets and looters raid delivery trucks daily. Medicines are also in short supply.

For a nation in dire economic straits, the Olympics could have offered a distraction from politics. Instead, they have mostly shown just how heavily politicized Venezuelan sport has become.

Benitez, who served as sports minister shortly after Chavez died of cancer in 2013, is among a group of pro-government athletes who have benefited from state support and who back Chavez's self-declared "son" and successor, Nicolas Maduro.

Maduro, in turn, has used the Olympics to score political points in marathon television appearances.

On Tuesday, the 53-year-old former bus driver praised triple jumper Yulimar Rojas, to whom he gave a new car in May, for her silver medal in Rio.

"A few years ago this girl was just peacefully in Barcelona (Venezuela), but the social program 'Mission Sports in the Slum' arrived, discovered her, and gave her all the world's support," Maduro said in a broadcast on state TV.

"Thanks to whom? To the Bolivarian revolution, our commander Chavez, and the sporting revolution."

Most of the nation's nearly 90 Olympic athletes depend on government sponsorship and support to get ahead, but some lack coaching and train with poor equipment. A few had to plead for donations to fund their trips to Brazil.

A spokesperson for the Venezuelan Olympic Committee did not respond to a request for comment.

STOCKING UP IN RIO

Most Venezuelan athletes have kept a low profile in Rio, preferring to focus on performance rather than politics. The nation has won three medals so far: one silver and two bronze.

In interviews with about a dozen of the athletes, several confessed to have something else on their minds, however: stocking up on food, medicines and other basic goods to take back home.

Beach volleyball player Norisbeth Agudo said family and friends had asked her for medicine and cosmetics while sailor Jose Gutierrez said he wanted to take home medicines.

"That's not the reason I'm here," said Gutierrez, who lives in the capital, Caracas.

"I'm here to think about the competition ... but of course I use the opportunity to bring home things that we need."

Many were reluctant to speak about such a politically sensitive topic.

"To avoid being controversial I would rather not speak about the subject," basketball player Gregory Echenique said. He described the situation in Venezuela as hard and said he had moved much of his family to the United States.

In contrast, Venezuelan fans who made the trip to Rio, despite a tanking home currency and a shortage of flights out of Caracas, spoke freely about filling their stomachs and their suitcases while in Brazil.

"I'm going to take advantage and eat everything I can't get there: salmon, bacalhau (cod) - it's been years since I've seen bacalhau over there - and a good barbecue," said Venezuelan Juan Carlos, 36, as he caught a basketball game, adding he would also be buying medicine and hygiene products.

For most of his compatriots back home, though, Rio's multi-billion-dollar sports extravaganza feels remote from the daily task of putting food on the table.

Carpenter Luis Colmenares said he slept through Maduro's Rio-themed broadcast earlier this month because he had to get to a supermarket by 4 a.m. the next morning in the hope of finding flour, rice, and cooking oil.

He waited 12 hours before being turned away empty-handed.

"I'm sure the athletes are guaranteed a good diet but the rest of the country is finding it very difficult to get hold of food," said the 40-year-old, adding that he had lost some 10 kgs (22 lb) in weight over the last few months.

"We just want to be able to get food."

(Additional reporting by Girish Gupta in Caracas and Jeb Blount, Paulo Prada, and Anthony Boadle in Rio; Editing by Mark Bendeich)