UNITED NATIONS (CNN) -- Georgia has asked the U.N. Security Council to discuss Russia's "military aggression" after saying a Russian jet shot down one of its unmanned spy planes.

"We call upon the United Nations to address this direct military aggression against Georgia and to fully exploit its own means and capabilities in order to keep the situation from further escalation," Georgia's U.N. Ambassador Irakli Alasania told reporters Monday.

To bolster its case, the Georgian air force released a video that it says shows a twin-tailed Russian MiG-29 shooting down a Georgian unmanned aerial vehicle, or UAV, over the separatist region of Abkhazia on Sunday.

The video -- shot by the drone, Georgia says -- shows a jet fighter firing a missile that streaks through the sky, trailed by a column of white smoke. The missile gets closer and closer and then suddenly the screen goes blank. Watch unmanned spy plane be shot down »

"The radar shows that the MiG-29 took off from Gudauta in Abkhazia, Georgia. It is absolutely illegal for a Russian MiG-29 to be there," Col. David Nairashvili, Georgia's air force commander, said. "The MiG-29 flies south, shoots down the Georgian UAV and then flies north crossing into Russian territory."

Georgia's charges come at a time of increasing tensions between the pro-Western government and Moscow, which is providing assistance to a pair of breakaway regions in Georgia -- Abkhazia and South Ossetia.

Without addressing the question of whether a Russian fighter flew over Georgian territory, Russian President Vladimir Putin said he was surprised by Georgian military flights over Abkhazia, Russia's Itar-Tass news agency reported Tuesday, blaming the flights for the escalation of tensions.

In a phone call with Georgian President Mikhail Saakashvili on Monday, Putin expressed "bewilderment over the very fact of military flights performed by the Georgian side over the conflict zone and stressed that this contradicts the letter and the spirit of the Moscow ceasefire and disengagement agreement of May 14, 1994," the news agency said.

Georgian forces fought separatists in Abkhazia before the ceasefire was negotiated more than a decade ago.

Last week, Moscow formalized relations with the breakaway territories, withdrawing trade sanctions and expanding "trade, economic, social, scientific and technical, information, cultural, and educational" contacts with them, Itar-Tass reported. E-mail to a friend

All About Abkhazia • Vladimir Putin