UPDATE 2-Russia's Putin wins approval for gas pipeline to EU

* Russia's Putin gets Slovenia to sign up to South Stream

* Putin says now has all EU deals needed for pipeline

* Approval paves way for Russian gas to flow to Italy

(Recasts, changes headline, dateline PVS MOSCOW)

By Gleb Bryanski

NOVO-OGARYOVO, Russia, Nov 14 (Reuters) - Russian Prime Minister Vladimir Putin won Slovenia's approval on Saturday for the South Stream pipeline, undermining European Union efforts to reduce dependency on Russian gas supplies.

The seal of approval is the latest victory for the Kremlin as it seeks to counter the long delayed Nabucco pipeline which is backed by the European Union as a way to curb dependency on Russia by pumping gas from the Caspian and the Middle East.

Slovenia's approval brings the South Stream pipeline a step closer to being built, though its backers -- Russian gas behemoth Gazprom (GAZP.MM) and Italy's Eni SpA (ENI.MI) -- still have to raise billions of dollars to finance the project.

"We have now signed deals with all the European partners needed for this project to be completed," Putin told reporters at his Novo-Ogaryovo residency outside Moscow after signing the cooperation deal with Slovenian counterpart Borut Pahor.