Georgian interior ministry officials said three Russian helicopters fired late on March 11 on the Kodori Gorge.
The gorge, which Georgian officials call Upper Abkhazia, is the only part of Abkhazia still under Tbilisi's control.
Russia's air force denied any attacks and said all its aircraft near the area were grounded over the weekend.
Saakashvili told the Security Council meeting that the incident created a grave situation. "This is a very dangerous, serious and far-reaching provocation aimed at disrupting order and changing the situation for the worse," Saakashvili said.
However, Saakashvili stopped short of pointing the finger at Russia directly. "I don't want to make accusations against one particular side. The [Georgian] foreign minister has received instructions to contact his Russian counterpart and firmly demand that Russia react to this situation."
The deputy commander of Russia's ground forces, Lieutenant General Valery Yevnevich, has said that helicopters cannot fly over the Caucasus mountain range. "From the Russian side, it is impossible for helicopters to find a passage to fly through because of the high mountains. Mount Elbrus is over 5,000 meters high. Helicopters cannot fly over the Caucasus mountain range for technical reasons," Yevnevich said.
Russian Foreign Ministry spokesman Mikhail Kamynin said that Russia was investigating the circumstances of the shooting, but noted that the air force said it did not conduct flights in the area at the time.
Abkhazia’s separatist leader Sergei Bagapsh denied any incident.
(with material from agency reports)
NOT ALL WINE AND ROSES. Moscow's relations with Tbilisi since the collapse of the Soviet Union have often been tense and strained. Among the issues that have made the relationship difficult are Moscow's alleged support for the breakaway Georgia regions of Abkhazia and South Ossetia, as well as the continued presence of Russia troops on Georgian territory. Periodically, Georgian lawmakers propose withdrawing from the Commonwealth of Independent States (CIS) altogether. RFE/RL has written extensively about the rocky relationship between these two countries.