"No one is being told his place of residence. This is done on his request because we understand that the level of danger is quite high," Anatoly Kucherena told RT television in an interview, the Interfax news agency reported ahead of the broadcast.
"I think it is still impossible to say or 'unscramble' his place of residence," Kucherena added.
Snowden has remained hidden from view since Russia granted him temporary asylum on August 1 and he left the transit zone of Moscow's Sheremetyevo airport where he had apparently been trapped since arriving from Hong Kong on June 23.
Kucherena said that Snowden had security guards, although he was evasive about whether they come from Russia's security forces.
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"They do not necessarily have to be Russian security forces. We have quite a few private firms," he said.
"He walks around. He can travel. He does travel, because he is interested in our history," Kucherena said.
Asked if people had recognised Snowden, he said: "No, so far no one has recognised him."
He confirmed that Snowden's father still planned to visit him, as did his mother and his grandparents.
"His mother will probably come too, and maybe his grandmother and grandfather," Kucherena said.
Snowden's father's US lawyer said in August that he had received a Russian visa, but Kucherena said there was a delay due to Lon Snowden's plans.
"Yes, undoubtedly. You have to understand that Edward worked quite a long time for the CIA. He is a good specialist. He is a professional."
Snowden's disclosures are continuing to trickle out in the British Guardian newspaper and other publications.
The United States wants Russia to hand over Snowden so that he can be investigated over the publication of details of mass surveillance carried out by the National Security Agency.