President Vladimir Putin has temporarily banned Georgian airlines from flying to Russia amid rising tensions between the two countries.
On Thursday, some 240 people were injured in protests in Georgia. The protests were ignited by the appearance of a Russian MP in the country's parliament.
Mr Putin signed a decree on Friday suspending flights to Georgia by Russian airlines.
The suspensions will start from 8 July.
A transport statement on Saturday said the reason for the latest suspension was to "ensure a sufficient level of air security and arrears" owed by Georgian companies.
The Kremlin said the suspension on Russian airlines flying to Georgia was to "ensure Russia's national security and protect Russian nationals from criminal and other unlawful activities."
Tensions between the countries remain high, 11 years after they fought a war over the region of South Ossetia.
On Saturday, a news team from Russian state TV was attacked by two men on the street in the capital, Tbilisi. Nobody appeared to have been seriously hurt in the incident, which was captured on film.
What other action is Putin taking?
Mr Putin has ordered plans to be made to help bring back Russian citizens already in Georgia.
Moscow also recommended that Russian travel agencies suspend all tours to Georgia.
Several thousand Russian tourists are currently in Georgia, Russian tour agency representative Maia Lomidze told Russian media. According to Russian data, about half a million Russians have visited Georgia to date this year while 1.7 million Russian tourists went there last year.
"Tourism in Georgia is on the rise, and the decision has shocked the whole industry," Aleksan Mkrtchyan, who runs a chain of Russian travel agents, said in a statement.
"Georgians have traditionally treated Russians well," Irina Tyurina, a spokeswoman for the Russian Tourism Union, told AFP News agency.
Deep frustrations on show
Analysis by Rayhan Demytrie in Tbilisi
Protesters gathered again on Friday night outside the Georgian parliament building where they have been chanting "No to Russia" over and over again.
But they have motives that extend beyond denouncing Moscow. These demonstrators want the Georgian Interior Minister Giorgi Gakharia to resign over his handling of the unrest.
They are also angry at how the police dealt with Thursday's protests. Tear gas, rubber bullets and water cannon were used to push back the crowd in what were ugly scenes.
And on Friday, protesters came out in bigger numbers. It appears the visit of a Russian MP has unlocked much deeper frustrations with the current administration and the way it has handled relations with its northern neighbour.
What caused the protests?
Sergei Gavrilov, the Russian MP who sparked the fury, had addressed an assembly of MPs from Orthodox Christian nations on Thursday.
He had been taking part in the Interparliamentary Assembly on Orthodoxy (IAO) - a body set up by the Greek parliament in 1993 to foster relations between Christian Orthodox lawmakers.
Opposition MPs in Georgia's parliament called for protests after he delivered his speech in Russian from the Speaker's seat.
"That was a slap in the face of recent Georgian history," Elene Khoshtaria, an opposition member of parliament, said.
Thousands of protesters tried to storm the parliament, and police used rubber bullets and tear gas in an attempt to disperse them.
Some protesters carried EU flags and placards reading "Russia is an occupier".
Giga Bokeria, an opposition MP for the European Georgia party, told AFP news agency the rally outside parliament had been "a spontaneous protest by ordinary Georgians".
The Speaker of the parliament, Irakli Kobakhidze, resigned following the violence.
Georgian President Salome Zurabishvili called Russia "an enemy and occupier", saying Moscow had helped to stir the unrest.
The Kremlin condemned the protests as "Russophobic provocation", while Russia's foreign ministry accused Georgia's opposition of trying to prevent an improvement in bilateral relations.
Why are there tensions between Georgia and Russia?
When Georgia declared independence from the Soviet Union in 1991, separatist conflicts erupted in the regions of Abkhazia and South Ossetia.
In August 2008, Georgia attempted to recapture South Ossetia. Russia poured troops in, ousting Georgian forces and only halting their advance within striking distance of Tbilisi.
Following a ceasefire, Russia withdrew most of its troops from undisputed parts of Georgia but still maintains a military presence in South Ossetia and Abkhazia, recognising both as "independent" states.
Since then, diplomatic relations between Russia and Georgia have remained clouded by mutual suspicion. Georgia has ambitions to join the European Union and Nato, a prospect viewed dimly by Russia.
However, bilateral trade and tourism had been growing in recent years.