"Yesterday I sent an invitation to Snowden's father, to his US lawyer and to the friends that Edward asked for," Snowden's lawyer Anatoly Kucherena told Kommersant FM radio station.
"The invitation has gone off, we are waiting for the visas to be processed."
The former National Security Agency analyst is living at an unknown location after Russia granted him temporary asylum for a year. He is wanted by the US for leaking details of vast Internet and telephone surveillance programmes.
Snowden now has registered at an address -- a legal requirement for foreign visitors to Russia -- Kucherena said, while declining to reveal any details of his new address.
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"He has registered" he told the Interfax news agency. "Today he is living on the territory of Russia."
Kucherena said that Snowden would probably consult his father on what to do with his new life in Russia.
"When his father, lawyer, friends come, I think all the important questions on his daily life and accommodation will be discussed," he told Kommersant FM.
Ryabkov accused the United States of "blowing up the situation with Snowden," insisting that Russia had avoided involvement in his case "beyond the absolutely humanitarian aspect."
Venezuelan Foreign Minister Elias Jaua on Tuesday reaffirmed his asylum offer to Snowden in an interview with Russian-based RT television network.