Sorokin's company operates in the Krasnodar region, which includes Sochi and the neighboring area. He refused to say how many dogs they kill a year, calling it a "commercial secret."
Sergei Krivonosov, a lawmaker from the Krasnodar region, last year supported the dog culling.
Krivonosov said taking the dogs off the street was Russia's "responsibility to the international community and that their elimination is the quickest way to solve this problem."
He conceded, however, that this is "not the most humane way" of dealing with the problem and that authorities should encourage dog shelters.
Sochi city hall last year announced a contract "to catch and dispose" of strays in Sochi — a move that animal activists vehemently protested. Authorities pledged to give up the practice and build animal shelters for strays instead.
Activists say there is no evidence that a shelter has been built. But city hall said in a statement on its website that it had opened a dog shelter Monday for 100 dogs.
Shooting stray dogs has been common practice in many Russian regions despite activists' efforts to push for more humane ways to deal with the issue.
Nadine Kincaid, an Olympic volunteer from Portland, Oregon, was surprised by how many dogs are roaming around Sochi.
"There's a lot of dogs everywhere. Right behind where we're staying, there's a whole legion of dogs," she said. "I come from a town where there's leash laws and everyone has to pick up after their dogs, so that's unusual to me to see that."
Kincaid said she would be upset if the dogs were being poisoned.
"As an animal lover, for me that's sad. But if they're like stray cats, they can keep breeding and cause more problems. So I can see, maybe, why," she added. "It's sad, but what do you do if you can't control them?"
Associated Press writer Leonid Chizhov contributed to this report.