Vyacheslav Sedov, a Russian defence ministry spokesman, said: "On the date mentioned by Georgia the planes of the Russian air force did not fly near to the Georgian border."
Georgia's foreign ministry said the aircraft had crossed into Georgia near its Black Sea coast and adjacent to the separatist region of Abkhazia.
Most of that region is controlled by separatists, but the foreign ministry said the overflight was in a corner of Abkhazia under Georgian control.
Moscow-backed Abkhazia is a regular source of tension between Georgia and Russia.
And relations have deteriorated further after Georgia said an airplane coming from Russia had violated its airspace and dropped a missile near a village on the border earlier in August.
Russia also denied any part in that incident and accused the former Soviet republic of making up the attack.
However, Georgia asked for the UN Security Council to investigate the first alleged airspace violation.
Relations between Russia and Georgia have been fraught since Mikhail Saakashvili, the US-educated president, came to power in Tbilisi three years ago, and moved Georgia out of Moscow's orbit.
Last year, Russia severed air, sea and postal links with its southern neighbour over a spying row.
Before that, Moscow had banned imports of Georgian wine and mineral water, both major sources of revenue, citing health concerns.