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, 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.