A Jewish family's claim to one of Austria's most famous artworks by Gustav Klimt is shaping up as a test of the country's restitution drive and willingness to right old wrongs.

The 34-metre-long (112-foot) and two-metre-high "Beethoven Frieze", a jewel of Jugendstil art, has been a Vienna tourism highlight since 1986.

But the heirs of former Jewish art collector Erich Lederer -- who fled to Switzerland during World War II -- say the Austrian state obtained the masterpiece through dubious means and are claiming it back.

"Our clients want a wrong to be redressed," lawyer Marc Weber told a press conference Thursday, two days after the Lederer family filed a claim for restitution with the Austrian culture ministry.

"It is also immensely important for Austria's international image how it deals with its own history in cases such as this," he added.

The case is the biggest since Austria in 2006 had to give up Klimt's prized "Portrait of Adele Bloch-Bauer" to heirs of the previous owner.

The latest restitution demand is also the most high-profile one to emerge under a 2009 restitution law, which covers not just Nazi-looted art but also art that was bought by the Austrian state after the war under sometimes dodgy circumstances.

"The 'Beethoven Frieze' is a textbook case for this new restitution law," according to legal expert Georg Graf, who wrote one of the reports laying out the case for restitution.

Seized by the Nazis, along with the rest of the Lederer family's important art collection, the fresco -- which depicts man's path to happiness -- was returned to Erich Lederer after the war.

But through "artful tricks" and an export ban, Austria compelled him to sell the work to the state in 1973 for less than half its worth, according to Graf.

Thanks to the 2009 law, the heirs now have a case, lawyers and experts agreed.

"By returning the 'Beethoven Frieze', Austria can set an example and take a leading international role in terms of restituting looted art," Weber said.

'An avant-garde law'

Amid strong international media interest, the culture ministry has been at pains to stress it wants nothing to do with illegally acquired art.

"The state has a responsibility," press spokesman Raimund Lang told AFP.

"I don't think anyone in Austria would say 'we want to keep this' if we obtained it illegally."

Aside from investigating restitution claims by third parties, Austrian authorities are also looking into the origins of all artworks in their possession.

"Under the 2009 law, everything is being checked," said Lang.

A restitution commission meets five or six times a year and publishes its recommendations online.

"An incredible number of collections have art or objects that they should not have," Eva Blimlinger, the commission's scientific coordinator, told AFP.

In November 2012, three paintings from a Vienna museum were returned to Erich Lederer's heirs.

"Austrian law, in the revision of 2009, is quite unique and in some way progressive," art historian Robert Jan van Pelt from Canada's University of Waterloo said.

"Austria is in a kind of avant-garde position vis-a-vis this particular problem... That's one of the reasons that people abroad will be looking at this (case), because it is one where not only legal history will be made but also history as such," he told journalists in Vienna.

No decision on a restitution will likely be taken before next year.

If the work is handed back, the heirs must then return what the state paid for it -- 15 million Austrian Schillings, or about $750,000 at the time -- Graf said.

Auction house Christie's estimated last month that the work was actually worth $2.0 million in 1973. Its current value is unknown.

The "Beethoven Frieze" -- inspired by the German composer's Ninth Symphony -- is seen as one of the masterpieces by Austrian artist Klimt, perhaps best known for his painting "The Kiss".

The large-scale 1902 work is housed at Vienna's Secession art gallery, the place for which the piece was originally conceived.

Whether it will remain on display in Vienna or elsewhere if it is returned to the Lederer family remains unclear, their lawyers said.