Shota Khizanishvili, the chief of staff at Georgia's Interior Ministry, denied any links between Georgia and Umarov.
"I can only say that the National Anti-Terrorist Committee is staffed with people with peculiar fantasies," Khizanishvili told the AP. "They're always trying to accuse Georgia and its secret services of everything in any situation and without any grounds. This is a sign of severe paranoia."
Georgia and Russia fought a brief but intense war in 2008, and distrust between the two countries still runs very high. Georgia has accused Russia of spying on its government and supporting a failed coup to topple pro-Western President Mikhail Saakashvili and has urged the world to boycott the Sochi Olympics.
Sochi's selection as the host of the games had sparked fears of terrorism, although Russia pledged to keep the Olympics secure.
The International Olympic Committee would not comment on the specific security case at Sochi but said in a statement that "security is a top priority for the IOC.
"Security at the games is the responsibility of the local authorities, and we have no doubt that the Russians will be up to the task," the statement said.
Misha Dzhindzhikhashvili in Tbilisi, Georgia, and sports writer Stephen Wilson in London contributed to this report.
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