Georgia and Russia have blamed each other for the outbreak of protests and unrest in Tbilisi which was sparked by the visit of a Russian MP to Georgia's parliament.
And in an exclusive interview with Euronews, Georgia's president Salome Zourabichvili has called for a "de-escalation" in the protesters' standoff with her government.
The call came as protesters gathered for a third night in the capital.
Zourabichvili had earlier blamed Russia for the unrest, suggesting a "fifth column" loyal to Moscow had stirred up trouble.
But Russian Prime Minister Dmitry Medvedev dismissed her claim as a distortion of reality.
"What this country needs more than anything else is quietness and internal stability because that's our real strength. There is a political problem with Russia and everybody hopes that this will be solved one day," Zourabichvili told Euronews.
Violence flared in the Georgian capital late on Thursday, where police used tear gas and rubber bullets to stop crowds furious about the visit of a Russian delegation from storming parliament.
Hundreds of people were injured, some seriously, as demonstrators pushed against lines of riot police, threw bottles and stones, and grabbed shields, drawing a tough response.
Though the protests began over Georgia's diplomatic relationship with Russia, opposition parties have also begun to call for wider reform.
Georgia and Russia fought a brief war over the provinces of South Ossetia and Abkhazia in 2008. The provinces remain under Russian military control even though the international community recognises them as part of Georgia.
Thousands gathered outside parliament where opposition leaders gave the floor to young activists and students.
Zourabichvili also hinted that the unrest was an attempt at destabilisng her country.
"There are attempts for destabilization and that is something that we should be very wary about and be careful. It is very easy in a country like this to play on the feelings of the population and to agitate those feelings," she told Euronews.
On Friday President Vladimir Putin signed a decree suspending Russian passenger flights from Russia to Georgia from July 8 to protect people from what the Kremlin called "criminal actions".
Putin also recommended Russian travel agencies suspend tours to Georgia and ordered the government to bring Russian tourists already there home.
On Saturday he also banned flights coming from Georgia to Russia.
Over one million Russian tourists holiday in Georgia each year and the bans are likely to significantly hit the tourist sector.