* EU to sign association accord with Georgia in June
* Georgia fought brief war with Russia in 2008
* No NATO, EU membership possible any time soon-Steinmeier
By Margarita Antidze
TBILISI, April 24 (Reuters) - France and Germany assured Georgia on Thursday that a deal bringing it closer to the European Union would be sealed within weeks, moving to tighten ties with the ex-Soviet republic as tension mounts between Russia and the West over Ukraine.
The two core EU nations' top diplomats affirmed plans to speed up the signing of a deal to boost trade and political ties - the same kind of pact whose rejection by Ukraine in November touched off the biggest East-West crisis since the Cold War.
"I am sure that by the end of June the agreement will have been signed and that it is an important milestone in the history of Georgian and European relations," German Foreign Minister Frank-Walter Steinmeier said in Tbilisi.
"This agreement is not aimed against anyone ... The EU's economic relations with Georgia don't place economic cooperation between Georgia and Russia in doubt," he told a joint news conference with French Foreign Minister Laurent Fabius.
Georgia has strategic importance because it is on the route of pipelines which carry oil and gas from the landlocked Caspian Sea, an alternative to Russian energy, to world markets.
Relations between Georgia and Russia were badly strained by a five-day war in 2008, when Moscow's forces drove deep into the small Caucasus nation. That war was partly a result of Tbilisi's drive to join NATO and to move closer to the EU.
Despite attempts by Moscow and Tbilisi to improve ties after a change of government in Georgia in 2012, they have still not restored diplomatic relations and last month Russia's annexation of Ukraine's Crimea region revived Georgian security concerns.
The United States and the EU have stepped up support for other former Soviet republics in a tug-of-war with Moscow.
Georgia and Moldova had been due to sign the EU "association agreement" by the end of this year, but in the light of the Ukraine crisis EU leaders agreed to aim to get the deals sealed by June because of fears they could come under Russian pressure.
"We don't see any contradiction between the signing of this agreement and Georgia's economic relations with other countries, particularly Russia," Fabius said, in comments clearly designed to reassure Moscow.
An abrupt decision last November by Ukraine's then-president, Viktor Yanukovich, to scrap plans to sign an EU association agreement and to turn instead towards Russia ignited street protests that finally drove him from power in February.
Russia then annexed Crimea in March in response to what it described as a criminal coup and has amassed forces near the Ukrainian border, reserving the right to send them in to protect Russian-speakers in eastern Ukraine if it sees the need.
Russian President Vladimir Putin warned Ukraine's pro-Western government on Thursday that deploying the army against its own people in eastern Ukraine would be a very serious crime that would incur "consequences".
On Wednesday, Steinmeier and Fabius also visited ex-Soviet Moldova, which like Georgia has tense ties with Moscow and has a Russian-backed separatist region on its territory.
Georgia's ambition of joining NATO has effectively been on hold since the 2008 war, but the Ukraine crisis has put back on the agenda the question of whether the nation of 4.5 million people might eventually be admitted into the Atlantic alliance.
Steinmeier said NATO would work out steps for closer cooperation with Georgia before a September summit, but signalled that membership of the alliance and of the EU would remain off the cards for a long while to come.
"We can't define today what will happen in 10, 15 or 20 years. We are now at the stage ahead of signing the association agreement with the EU that is very important," he said, speaking through an interpreter. (Reporting by Margarita Antidze; Editing by Steve Gutterman and Gareth Jones)