The move on Saturday followed an outbreak of unrest in Georgia’s capital, Tbilisi, triggered on Thursday by a Russian legislator’s address in the former Soviet nation’s parliament.
“The reason for this suspension is the necessity to ensure a sufficient level of air security and arrears” owed by Georgian companies, a statement by the Kremlin said.
On Friday, Putin signed a decree banning Russian airlines from flying to Georgia, saying the ban was to “ensure Russia’s national security and protect Russian nationals from criminal and other unlawful activities”.
The Kremlin also recommended travel companies stop selling holiday packages to Georgia and advised Russian tourists visiting the country to return home.
In Tbilisi, hundreds of people demonstrated before the Georgian parliament for a third straight day on Saturday, though their numbers were visibly smaller than the tens of thousands who had protested in previous days.
TV footage showed protesters peacefully calling for Interior Minister Giorgi Gakharia to quit, saying he should take responsibility for heavy-handed police action during Thursday’s demonstrations.
The clashes between police and protesters injured at least 240 people on Thursday, including two reported to have lost eyes when police fired rubber bullets to try to disperse protesters, who had been attempting to storm the parliament building.
The crowds had been calling for the chairman of the parliament, Irakli Kobakhidze, to resign.
He was held responsible for a controversial visit by a Russian delegation, including the legislator Sergey Gavrilov, who addressed an assembly of MPs from Orthodox Christian countries from the seat of the speaker.
Kobakhidze responded by quitting his job on Friday.
A large but more orderly protest was held on Friday, with demonstrators denouncing the government as overly friendly to Russia and calling for a snap parliamentary election.
Anti-Russian sentiments run high in Georgia as Russian troops occupy about 20 percent of the Georgian territory, including breakaway regions of South Ossetia and Abkhazia, since the break-up of the Soviet Union in the 1990s.
Moscow has suspended flights to Georgia before – during a spike in tensions in October 2006 and in August 2008 following the outbreak of a five-day war over Abkhazia and South Ossetia.
Following the conflict, Russia recognised the independence of both separatist regions.
Georgian President Salome Zurabishvili called Russia “an enemy and occupier” and suggested Moscow had helped trigger the protests, while the Kremlin on Friday blamed radical Georgian politicians for what it called “an anti-Russian provocation”.