* State to get up to 49 pct stake in Volksbanken after rescue
* Increased bank levy to offset state costs of bailout
* New owner for stake to be found by 2017 - Fekter
* Kommunalkredit Greek exposure poses next hurdle (Adds quotes and background)
VIENNA, Feb 28 (Reuters) - Austria aims to sell by 2017 the big minority stake in Volksbanken AG it will get by rescuing the ailing lender in a bailout funded by fellow banks, Finance Minister Maria Fekter said.
Austria would also have to help nationalised lender Kommunalkredit sort out its Greek debt exposure this year, she told reporters on Tuesday.
Austria will take a stake of up to 49 percent in Volksbanken in a rescue that will cost the state more than 1 billion euros ($1.3 billion) in writedowns, fresh capital and guarantees.
Chancellor Helmut Faymann said a second bailout for Volksbanken - it had already got 1 billion in state capital - was cheaper than letting the lender go bust. A failure would have triggered deposit insurance claims and state guarantees.
"We were talking about an overall risk of 13 billion euros," Faymann said after a cabinet meeting.
Losses on Greek debt and bad loans in eastern Europe have hammered Volksbanken, once the country's fourth-biggest bank which failed last year's European stress tests.
It forecast in November its 2011 loss would be at least 10 percent greater than the consolidated 500-750 million euros it had expected only a month before.
The 62 regional banks that own a Volksbank majority are also injecting fresh funds, while minority shareholders DZ Bank Group , insurer Ergo and Raiffeisen Zentralbank will see their stakes diluted sharply.
Ratings agencies have cited Austria's relatively large financial sector as a risk to its sovereign debt rating. Standard & Poor's has already stripped Austria of its AAA rating and Moody's has said it might do the same.
FAIR IS FAIR
Austrian officials put the best face on taking a third bank under the state's wing after the emergency nationalisations of Kommunalkredit and Hypo Alpe Adria in 2008 and 2009.
Fekter said the bailout would have no impact on Austria's drive to consolidate state finances because it would finance its costs by increasing a special levy on banks it adopted in 2011.
Raising the bank tax by a quarter until 2017 is set to bring in an extra 750 million euros.
Big Austrian lenders include Erste Group Bank, Raiffeisen Bank International (RBI) and its unlisted parent Raiffeisen Zentralbank, and Italian group UniCredit's Bank Austria unit.
Most banks declined comment on the increased hit, which RBI estimated would cost it around 20 million euros more a year.
"It is simply a matter of fairness that the sector that benefits from stability in the financial sector also makes a contribution," Deputy Finance Minister Andreas Schieder told Austrian radio, adding competition among banks would prevent them from passing the levy on to customers.
Shares in Austrian banks were mixed by 1240 GMT while spreads for 10-year government bonds over benchmark German Bunds were little changed at around 115 basis points.
Fekter reiterated that Austria was ready to stand by Kommunalkredit as it digests losses on Greek debt holdings.
"We know that there are Greek securities at Kommunalkredit and, in the course of its restructuring, Kommunalkredit will also need money. Precautions have been taken for this and this is something we will have to process this year," she said.
KA Finanz, the so-called bad bank split off from Kommunalkredit, will likely need more help to handle writedowns on its nearly 1 billion euros in Greek debt exposure.
Kommunalkredit Austria, the "good" part of the lender, has said it could weather any hit on its Greek debt holdings without more state aid.
The bank tax introduced last year aims to raise around 500 million euros annually. It is based on lenders' adjusted total assets and ranges from zero for less than 1 billion euros assets to 0.085 percent for assets over 20 billion. ($1=0.7466 euro) (Additional reporting by Angelika Gruber; Editing by Mike Nesbit and Dan Lalor)