Russia has committed an "act of aggression" against Georgia by firing a guided missile at its territory, officials in Tbilisi say.
Georgia said no-one was injured in the incident
They say the missile landed outside the village of Tsitelubani on Monday, some 60km (37 miles) north-west of the capital Tbilisi, but did not explode.
Georgia has now made a formal protest to Russia over the incident. Moscow denies all the accusations.
Relations between the two countries have been strained in recent years.
Moscow is angry about Georgia's plans to join Nato, while Tbilisi accuses Russia of trying to destabilise Georgia.
Georgian officials say two Russian "Su-type" jets launched the missile at 1930 (1530 GMT) on Monday.
Interior Ministry spokesman Shota Ustiashvili told the BBC the planes had flown some 70km (43 miles) over Georgia, firing the "modern and powerful" rocket, which weighed about a ton.
Mr Ustiashvhili said the jets flew from a Russian base in the North Caucasus before firing the missile, which landed just metres from a house.
Local resident Ilia Psuturi told Reuters news agency: "I was sitting in my garden... when I saw a plane in the sky.
"I then saw smoke rising from the ground up to the sky and only then did I hear the explosion. The plane then turned around," he said.
Georgian officials said they had gathered fragments of missile fins and other debris near a small crater where the rocket landed.
"It has become common practice for the Russian air force and for the government troops to sneak into the Georgian territory," Mr Ustiashvili said.
"But what is different in this incident... is that they have threatened Georgian airspace much deeper, and that they have used a very powerful bomb."
Georgian Foreign Minister Gela Bezhuashvili told the BBC the missile firing was an "act of aggression".
He said foreign diplomats in Georgia were being asked for a "stronger and clear-cut response" to the incident from the international community.
South Ossetia theory
Earlier on Tuesday, Georgia's foreign ministry handed a note of protest to the Russian ambassador in Tbilisi, although Moscow continued to deny all accusations.
"Russia's air force neither on Monday nor Tuesday flew flights over Georgia," said Col Alexander Drobyshevsky, an aide to the commander of Russia's air force.
"Russia has not violated the borders of sovereign Georgia."
Tsitelubani is not far from Georgia's breakaway region of South Ossetia, which receives political support from Moscow, says the BBC's James Rodgers in Moscow.
South Ossetia's leader Eduard Kokoiti said Georgian planes fired the missile to discredit Russia.
"This is a well-planned provocation," said Mr Kokoiti, who holds Russian citizenship.
But a Russian defence analyst, Alexander Golts, said that without objective, hard information on the incident, it was impossible to lay the blame on either Russian or Georgian aircraft.
"While no one can say for sure whether it was a fuel tank or a rocket or a bomb which fell, I fail to see why a Russian plane would bomb territory close to South Ossetia," he told the BBC News website.
The conflicting accounts of the incident reflect ongoing tensions between Georgia and Russia, our correspondent says.
Relations between Moscow and Tbilisi deteriorated sharply last year when Georgia expelled four Russian army officers it accused of spying.
The deportation triggered a furious diplomatic row, with Moscow imposing economic sanctions against its neighbour and deporting a number of Georgians.
Georgian officials have frequently claimed that Russian military aircraft have violated its airspace - accusations always denied by Russia.
The worst problems have usually been related to regional conflicts - the frozen conflicts in South Ossetia and Abkhazia.
Many Georgians accuse Russia of imperialism, while Russia criticises Georgia for nationalism and pursuing an anti-Russian foreign policy.