The EU "expressed its grave concern at the measures adopted by the Russian Federation against Georgia and at their economic, political and humanitarian consequences" in a statement after a foreign ministerial meeting of the 25-member alliance.
Since four Russian officers were detained in the Georgian capital, Tbilisi, for alleged spying in late September and released soon afterwards, Moscow has suspended travel and mail links with the South Caucasus state and deported at least 300 Georgian for violations of immigration laws.
Moscow authorities have also launched a crackdown on businesses allegedly related to the Georgian mafia, which resulted in the closure of a number of gambling outlets and restaurants. Media outlets also report that Moscow police have instructed schoolteachers to identify pupils with Georgian surnames in order to check on the legality of their families' residence in Russia.
But the EU said both countries were responsible for the recent spat, and called on them to tone down mutual rhetoric.
"The Georgian leadership should avoid any action that could heighten the tensions," said the EU External Relations Commissioner, Benita Ferrero-Waldner.
EU foreign policy chief Javier Solana, who described Russia as Europe's strategic partner, said the EU will keep a balance in its contacts with Russia and Georgia. But he promised to raise the issue at an informal energy summit with Russia, Europe's major natural gas and oil supplier, Friday.