Already, hundreds of animals have been killed, with the local authorities apparently wanting the stray dogs cleared from the streets before Friday’s opening ceremony.
While the authorities say the dogs can be wild and dangerous, reports of their systematic slaughter by a pest removal company hired by the government in recent months have outraged animal rights advocates and cast a gruesome specter over the traditionally cheery atmosphere of the Games.
The handling of the matter has also sharply undercut the image of a friendlier, welcoming Russia that President Vladimir V. Putin has sought to cultivate in recent months.
“We were told, ‘Either you take all the dogs from the Olympic Village or we will shoot them,’ ” said Olga, who is coordinating the rescue effort on behalf of a charity called Volnoe Delo (roughly, Good Will), which is financed by Oleg V. Deripaska, one of Russia’s billionaire oligarchs.
A “dog rescue” golf cart is now scouring the Olympic campus, picking up the animals and delivering them to the shelter, which is really an outdoor shantytown of doghouses on a hill on the outskirts of the city. It is being called PovoDog, a play on the Russian word povodok, which means leash.
Lying past a cemetery, at the end of a dirt road and without electricity or running water, the makeshift PovoDog shelter is already giving refuge to about 80 animals, including about a dozen puppies. One is a chocolate-colored Shar-Pei and her two mostly Shar-Pei puppies. Another is a large, reddish-brown sheep dog named Kasthan, who likes to jump up and kiss the shelter workers, who are mostly volunteers.
Local animal rights workers say many of the strays were pets, or the offspring of pets, abandoned by families whose homes with yards were demolished over the past few years to make way for the Olympic venues and who were compensated with new apartments in taller buildings, where keeping a pet is often viewed as undesirable.
They also say that Russia has never made a priority of pushing responsible animal control policies, including spaying and neutering, which would have helped avoid the current problems.
“We need a program of sterilization for dogs,” said Nadezhda Mayboroda, a Sochi resident who is working at the shelter. “People are not really well educated that it is necessary to sterilize their dogs at home. Human beings are not responsible at all.”
In recent months, residents of Sochi have reported seeing dogs shot with poisoned darts, then tossed into waiting trucks. Aleksei Sorokin, the director general of a pest control business, Basya Services, has confirmed that his company has been hired to catch and kill strays, telling local journalists the work was necessary.
The effort to remove the dogs began in October 2013, as did initial efforts to gather up strays and shelter them. Tatyana Leshchenko, an animal rights advocate here, said about 300 dogs a month were being killed in Sochi, at a cost of $25 to $35 each.
“It’s very cruel,” Ms. Leshchenko said, adding that the dogs were being shot with a chemical that causes them to suffocate. She said she had convinced at least one exterminator to give her advance warning of the neighborhoods to be cleared.
The International Olympic Committee responded with a carefully worded statement; Mark Adams, a spokesman, told reporters at a briefing Wednesday that no healthy dogs found on the grounds of the Olympics were being destroyed.
“It would be absolutely wrong to say that any healthy dog will be destroyed,” Mr. Adams said.
Humane Society International, an advocacy group based in Washington, wrote to Mr. Putin and urged him to prevent the killing of dogs, noting that the Russian president is also a dog lover. Mr. Putin has been photographed numerous times with his black Labrador, Koni.
It is true that there are stray dogs in Sochi, more stray dogs than in other cities. The explanation is quite simple. When a big construction project is underway, dogs and puppies always appear whom the builders feed. Now the builders have left, but unfortunately, the dogs remain.
Stray dogs have been found inside sports venues and have even wandered into some of the residences for Olympic athletes and visiting journalists. Dogs can also be found throughout the city and in the mountain areas where skiing and other outdoor events will take place. The Olympic Committee does not have responsibility for areas outside its official venues.
As thousands of fans streamed into the new Fisht Olympic Stadium for a dress rehearsal of the opening ceremony, what caught Ms. Melnikova’s eye was a Rottweiler sitting nearby.
Ms. Melnikova, who has two dogs of her own back home in Moscow, seemed heartbroken that she was unable to rescue the dog.
“On the left, near where the food court is, he was sitting next to the garbage container,” Ms. Melnikova said. But she was not prepared. “I need equipment to take a Rottweiler,” she said. “I didn’t have a collar. If I had a collar, I would have tried.”
Mr. Deripaska, an industrialist who largely made his fortune in aluminum, provided $15,000 to get the shelter started on land donated by the local government. He has also pledged about $50,000 a year for operations. He was also one of the major investors in the Sochi Games and paid for several huge projects, including an overhaul of the airport, a new seaport and the Olympic Village along the coast.
With the Olympics fast approaching, however, there was simply no time to build an indoor space for the shelter, especially because so much work remained to be done on hotels and other buildings for the Games.
“In Sochi, you just can’t find a construction guy because they are in such a rush to finish all the objects,” Ms. Melnikova said.
As local residents have learned of the shelter, however, the needs are only growing. On Tuesday night, shelter workers said, someone dropped off two puppies without any explanation or instruction. So far, the workers said, there have been some offers of money but few donations of what is needed most: food, veterinary medicines and other supplies, including dog shelters and collars.
All of the dogs entering the shelter receive medical treatment, including vaccinations. All of them will be eligible for adoption, even to fans attending the Olympics. Spared execution — at least for the moment — the animals at the PovoDog shelter barked in a loud chorus as the sun slowly dropped into the Black Sea, which could be viewed in the distance.
Many scampered around and nipped at each other, while one unlucky fellow got his head stuck in the chicken wire surrounding the shelter, only to be freed by a shelter volunteer, beseeching him to stay calm.
Tiny puppies squeaked and squawked. Workers said they were likely to find homes faster than the older dogs — two siblings of the Shar-Pei puppies have already been adopted.
Still, most of the dogs are mutts, and Ms. Mayboroda said many people would not be interested — a view that the shelter workers hope to change through a new publicity and outreach effort. “Everybody here wants a shepherd or a pit bull,” she said. “Nobody wants just a mixed dog.”