Georgia asked the United Nations Security Council on Wednesday to convene an extraordinary meeting to discuss the April 20 incident over Abkhazia.
Earlier Russian UN envoy Vitaly Churkin said Abkhazia should be invited to attend the session.
"We believe that without inviting Abkhaz representatives, the discussions will not be sufficiently serious, complete, or objective," Churkin told reporters, adding that Russia was not against holding the session.
In a report released on Monday, the UN mission in Georgia backed Georgia's claim that the drone was shot down by the Russian Air Force over Abkhazia. Russia says the video footage provided by Georgia as evidence was doctored, while Abkhazia says its own military shot down the Georgian drone.
Moscow has accused Tbilisi of violating a ceasefire agreement by sending spy planes into the conflict zone, where it has maintained peacekeeping troops since the end of a bloody conflict in the region in the early 1990s.
The UN report also criticized Georgia for carrying out reconnaissance flights over Abkhazia, saying such flights breach the terms of a ceasefire deal that ended a conflict in the early 1990s.
Abkhazia and Georgia's other breakaway territory, South Ossetia, are currently the main source of tension between Georgia and Russia, with Tbilisi accusing Moscow of trying to annex the territories. Tensions have also been fueled by Georgia's plans to join NATO.
Abkhazia and South Ossetia broke away from Georgia following the collapse of the Soviet Union.
Moscow recently bolstered the number of its peacekeepers in Abkhazia in response to Georgian troop buildup, but said the increase was still within previously agreed limits of 3,000 soldiers.
