European Council President Donald Tusk says Russia's move to ban direct flights to Georgia was "unjustified and disproportional."
Relations between Russia and Georgia came under additional strain three weeks ago when protests broke out in Tbilisi over a visit by a Russian lawmaker. Many protesters said they were angry about the continued presence of Russian troops on Georgian soil.
Georgia fought and lost a short war against Russia in August 2008.
Russian President Vladimir Putin ordered the flight ban on June 21, a day after the start of the protests in Tbilisi, citing risks to its citizens. The move threatens to hurt Georgia's tourist industry since over 1 million Russians visit each year.
Tusk said that the European Union was ready to support Georgia to withstand current challenges.
"The EU stands with Georgia in solidarity and with a full commitment to your sovereignty and territorial integrity," Tusk said at a conference in the Georgian Black Sea resort city of Batumi dedicated to the 10th anniversary of the Eastern Partnership, an EU initiative which works with Armenia, Azerbaijan, Belarus, Georgia, Moldova, and Ukraine.
He added that Brussels' relations with Georgia, which wants to join both the EU and NATO, were built on common values.
"After today's meetings I feel that Georgia has a very good and encouraging future," Tusk said.
Russia and Georgia have not had diplomatic ties since the 2008 war, and Russia went on to recognize the independence of two breakaway Georgian regions, South Ossetia and Abkhazia, where Russian troops are now stationed.
Georgian President Salome Zurabishvili said that occupation of the Georgian regions by Russia was "a frustration that is in the long term a matter for further instability."
"The reaction of the Georgian population is a sign that has to be considered here and by our partners," Zurabishvili said after meeting Tusk.