Five members of punk group Pussy Riot and a cameraman were attacked by Cossack security patrols as they performed under a sign advertising the Winter Olympics on Wednesday.
Footage showed the Cossacks whipping band members, pulling off their ski masks, and throwing them to the ground.
“The girls came here specifically to provoke this conflict,” Dmitry Kozak said.
“They had been searching for it for some time and finally they had this conflict with local inhabitants.”
Security in Sochi was a major concern before the Olympic Games following two suicide bomb attacks in Volgograd, in which 34 people died.
But Dmitry Kozak said he had always had confidence in security staff ensuring the Games remained safe.
The security procedures included hiring Cossack patrols to help police during the Olympics.
“We were certain that our security forces would be able to complete the tasks given to them,” he said.
“Security threats today are of a global nature, with terrorist organizations, so of course we were concerned about that.
“The Olympic Games became a target for the terrorists, but our law enforcement agencies and our special forces, in co-operation with all the countries of the world, all the special services in the world, including Great Britain, joined in the effort to prevent terrorism. All of us have fulfilled this task brilliantly.”
Dmitry Kozak also dismissed allegations of corruption and embezzlement in relation to money spent on the Games, which are estimated to have cost $50 billion.
“We had tough control over the budget money,” he said.
“According to the results of the investigation we did not find any major incidents of corruption.
“We ask anyone who says that there is to provide specific fact of the corruption. If they do we will carry out investigations and, if proved, the culprits will be punished. But so far we do not have this information, so it is just speculation.”
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