* Moldova and Georgia to sign agreements with EU
* Russia fears losing influence in both countries
* Barroso visits region, hopes to reassure Moscow (Adds info from Georgia)
By Alexander Tanas and Margarita Antidze
CHISINAU/TBILISI, June 12 (Reuters) - The head of the European Commission urged Russia on Thursday not to stand in the way of Moldova and Georgia forging closer ties with Europe, despite the conflict caused by Ukraine's lurch towards the West.
The two former Soviet republics plan to sign an "association agreement" on trade and political relations with the European Union on June 27 - a move which Moscow fears will take both countries further out of its sphere of influence.
Visiting the capital Chisinau to show solidarity with Moldova, Jose Manuel Barroso, president of the EU executive, delivered a speech that made no mention of Ukraine but sought to assure Russia that it had no reason to feel threatened.
"The association agreement is a positive agreement meant to add more momentum to Moldova's established international relations, not to compete with or intrude on Moldova's relations with any of its other partners, in particular Russia," he told an investment conference.
A more stable, secure and prosperous Moldova would benefit Russian producers and investors, he added.
"So I call upon Russia to take advantage of the new opportunities and not to take punitive measures further to the upcoming signature and implementation of the agreement with Moldova. There is no economic reason nor legal justification for such behaviour," Barroso said.
In the Georgian capital Tbilisi later on Thursday Barroso said that forging closer ties with Europe, including joining a free trade zone, would help bring prosperity and stability. He expressed hope that Russia would not put any obstacles in the ex-Soviet republic's way.
"Russian President Mr. (Vladimir) Putin told me and my colleague, European Council President Van Rompuy that Russia was not intending to have any kind of negative action on Georgia, when Georgia signs this agreement with the EU," Barroso told a news conference with Georgian President Georgy Margvelashvili.
"I hope that President Putin will stand by his own word."
Barroso has also appealed to Russia to "engage constructively with Ukraine and to propose concrete steps to de-escalation efforts."
Russia has flexed its muscles less over Moldova and Georgia than it did last year over Ukraine's plans to sign up for an association agreement with the EU.
Under Russian pressure, Ukraine's president at the time spurned the pact. But that sparked that protests that toppled him and led to the crisis in which Russia annexed Crimea and pro-Russian separatists have risen up in east Ukraine.
Russian Deputy Foreign Minister Grigory Karasin signalled Moscow's displeasure to Moldovan Prime Minister Iurie Leanca during talks on Tuesday, warning of "complications" in economic ties and a "serious test for them."
Similarly, Russian Foreign Ministry spokesman Alexander Lukashevich warned Georgia last month of "possible consequences" of signing the agreement with the EU.
Moldova, with a population of just over 3.5 million, and Georgia, which has 4.5 million people, see the signing of an association agreement as a crucial step towards mainstream Europe and eventual membership of the powerful EU trading bloc.
Moldova, which lies between Romania and Ukraine and has no border with Russia, fears Moscow might impose visa requirements on Moldovan citizens working in Russia or extend a ban on imports of Moldovan wines to include fruit and vegetables. It is also heavily dependent on Russia for energy supplies.
It is also concerned that Russia could foment unrest in Transdniestria, a Russian-speaking strip of land running down Moldova's eastern border with Ukraine where opposition to the pro-Western policies of the Chisinau government runs strong.
Georgia, which borders southern Russia but has no frontier with the EU, is wary of Moscow's political intentions six years after their five-day war in 2008 over two breakaway regions.
Georgian politicians fear Russia might now try to absorb those regions, Abkhazia and South Ossetia, following the annexation of Crimea from Ukraine.
Russia says it recognised the two countries' right to sign the association agreements, but Foreign Minister Sergei Lavrov is scheduled to visit Chisinau on either June 17 or 18, giving him a last chance to spell out Moscow's view. (Reporting by Alexander Tanas and Margarita Antidze, Writing by Timothy Heritage and Margarita Antidze, Editing by Hugh Lawson)