Georgia has demanded that the United Nations Security Council hold an emergency session to discuss what the foreign ministry describes as "a bombing".
Gela Bezhuashvili, the Georgian foreign minister, said: "We are continuing to gather proof. We have just received civil aviation radar recordings that confirm the military recordings."
He also claimed that an Organisation for Security and Co-operation in Europe investigation had found that Georgian airspace was violated.
Russia's air force has denied that its jets crossed into Georgia's airspace. Moscow called the incident an "attempt to derail positive trends in Russian-Georgian relations and exacerbate the situation with the settlement of the Georgian-Ossetian conflict".
The commander of a Russian-led peacekeeping force in the breakaway region of South Ossetia has suggested that a Georgian aircraft dropped the missile after coming under fire from the ground.
Tbilisi said its air force does not have Su-24 jets or missiles of the type found.
Georgia has accused Russia of trying to destabilise the country and of supporting separatists in South Ossetia and Abkhazia, another breakaway province.
The Gori region, where the missile was dropped, is next to South Ossetia.
The United States and European Union have urged restraint and called on both sides to resolve the incident.
Sean McCormack, US state department spokesman, said: "There have been previous attacks and whoever was responsible for this particular attack, these sort of provocations need to end."
The incident is the latest setback in bitter relations between Tbilisi and Moscow.
When Georgia arrested four Russians on spying charges in 2006, Moscow responded with sanctions against its tiny neighbour.
Some restrictions have been eased, but leaders of the two nations have continued to criticise each other.