The ministry also said that the flight over Abkhazia violated UN ceasefire agreements.
Speaking after the council discussed Georgia's request for an emergency meeting on Monday afternoon, Vitaly Churkin, Russia's UN ambassador, said: "We did not object to having a meeting ... and we'll have things to say at that meeting as well".
Churkin said that he reminded the council of the need to hear the views of the Abkhazian side.
"We will continue to work having them invited to speak to the council," he said.
Tensions between the two countries have escalated over two breakaway regions in Georgia - Abkhazia and South Ossetia - which have close ties to Moscow and have been independently run since the early 1990s when fighting with Georgian troops ended.
Officials in Tbilisi released footage on Monday that they said came from the drone's onboard camera and showed a Russian military MiG-29 jet launching a missile at the aircraft.
A spokesman for Russia's air force said that the allegations were "nonsense".
"What would a Russian jet fighter be doing over Georgian territory?" he said.
Mikhail Saakashvili, Georgia's president, said that he had telephoned Vladimir Putin, his Russian counterpart, to protest against "these aggressive attacks on Georgia".