UPDATE 1-Russia says near S.Stream deal with Austria, Slovenia

* Deal at "advanced level of preparation"

* Wants EU to make South Stream a priority project

* Slovenia says will sign the deal in June (Updates with Slovenian minister in paras 2, 3 and 10)

KHABAROVSK/LJUBLJANA, Russia, May 22 - Russia is close to securing Austrian and Slovenian participation in its South Stream pipeline to supply gas to Europe, Energy Minister Sergei Shmatko said on Friday.

Slovenia will sign the deal in June, Slovenian Economy Minister Matej Lahovnik said in Ljubljana on Friday.

"Slovenia has decided and wants to be a part of the project, we are working on the final text of the agreement, I expect that deal would be signed in June," Lahovnik told a news conference. Russia also wants to make South Stream a "priority project" for the European Union, Shmatko told reporters following an EU-Russia summit in the far eastern city of Khabarovsk.

"In the last two or three weeks, we've held a series of negotiations with Austrian and Slovenian partners about an intergovernmental agreement," Shmatko told reporters.

"This document is at an advanced level of preparation."

Russia last week secured support for its South Stream project from Italy, Bulgaria, Greece and Serbia. Moscow wants to outpace the rival, Western-backed Nabucco pipeline, which would supply gas from sources other than Russia.

Shmatko said Russia and its European partners in the project would request that Brussels grant it priority status.

"We agreed with EU Energy Commissioner Andris Piebalgs that Russia once more, together with its European partners in the project, would prepare a circular for the European Commission about affording the project such status," Shmatko said.

Lahovnik also said Nabucco remained an important project of the EU but added the question was whether there would be enough gas supply available for the Nabucco project. Slovenia has been a member of the EU since 2004.