Georgia requested the session on July 10 in response to an admission by Russia on the same day that its fighters had flown over the breakaway Georgian territory of South Ossetia two days earlier.
Russia said it had carried out the flights over fears that Georgia could invade the de facto independent republic. Tbilisi called the flights an act of "military aggression," and recalled its ambassador from Moscow.
On Monday, shortly after the Security Council had met, Russia's envoy to the UN, Vitaly Churkin, commented that "Certain countries did not manage to overcome an inclination toward a pro-Georgian position."
He also said that Russia had again raised the issue of the worsening situation in South Ossetia and Abkhazia, another Georgian breakaway republic. He repeated Russia's call for Tbilisi to sign a non-aggression agreement and to withdraw its troops from the upper part of the Kodori Gorge.
The Georgian envoy to the UN, Irakli Alasaniya, told journalists that, "We consider that Russia, as an influential regional power, should play a role in the peace process. However, this should not be a dominating role, including in the make-up of the peacekeeping contingent."
Georgia wants to replace Russian peacekeepers in Abkhazia with an EU non-military police contingent.
The U.S. envoy to the United Nations, Zalmay Khalilzad, said that Washington was concerned over the Russian incursion into Georgian airspace, calling it a violation of international law.
Other envoys declined to comment, although a source said that envoys from the EU had sided with the U.S. during the closed session.
South Ossetia declared its independence from Georgia following the collapse of the Soviet Union in 1991. Hundreds died in the bloody conflict that followed. The pro-Western Georgian leadership has said it is determined to bring the region, along with Abkhazia, back under central control.
Both South Ossetia and Abkhazia have been the source of rising tensions between Georgia and Russia since Moscow stepped up support for the breakaway republics in April. Recent events have involved explosions and shootouts in Abkhazia as well as the brief arrest of Georgian officers by South Ossetia.
South Ossetia rejected on Saturday an EU proposal to hold talks in Brussels on its current conflict with Georgia. A German peace plan for Abkhazia, backed by the EU, was rejected by the Abkhaz leader on Friday.