The Belvedere museum said on Friday it was following recommendations from the Austrian Interior Ministry and an insurance company in response to the threat.
A court last week ordered the state to return the five paintings to Maria Altmann, heiress of Ferdinand Bloch-Bauer, a rich Austrian industrialist whose possessions were expropriated the Nazis.
Altmann's American lawyer received the threat to destroy the paintings by email, the museum said.
The paintings, by turn-of-the-century Secessionist Klimt, are seen as masterpieces of Austrian public collections.
The five works are worth an estimated 200 million euros, including "at least 100 million euros" for the 1907 piece "Portrait of Adele Bloch-Bauer I," and "at least 60 million euros" for the "Portrait of Adele Bloch-Bauer I," completed in 1912, according to Altmann's lawyer Randol Schoenberg.
Austria, without a right of preemption, negotiated an option to buy back some or all of the five paintings by May, Schoenberg said Wednesday. He said such a buyback was however "unlikely," as Culture Minister Elisabeth Gehrer had said the price of the paintings "far surpassed" the financial capability of the republic, whose 2005 acquisition budget was 70 million euros.
"We are conducting intense negotiations to at least keep the two Adele Block-Bauer portraits” Gerbert Frodl, director of the Belvedere museum, told AFP Wednesday. "The specifics still need to be resolved," said Frodl, who spoke of "a great loss for Austria and Austrian culture."
Gehrer's comments have been severely criticized in Austria. Frodl said they did not facilitate" the search for sponsors and the daily Kurier said the minister "was failing to take into account why tourists come and spend their money in Vienna," whose cultural scene is the city's main tourism asset.
However, an amicable agreement between Austria and the 89-year-old Altmann seems out of the question after an almost six-year legal battle.
The Austrian-born Altmann is in favor of keeping the works in Austria but told the daily Die Presse the state "did not deserve" a financial gesture or loan on her part, as suggested by Gehrer.
Altmann proposed an amicable deal to the Austrian government in 1999 but received no reply. She then took legal action in the United States, which cost Austria 3.5 million euros (4.25 million dollars) before the two parties decided in May 2005 to resort to an arbitration court in Vienna.
The opposition Social Democrats (SPOe) said the government had a "negligent and incorrect" attitude and could have bought the paintings at a better price.
The city of Vienna also said buying back the paintings was a "moral duty".
The president of the National Assembly (Nationalrat), the conservative Andreas Khol, said Wednesday however the masterpieces should be bought without using public funds.
Among potential sponsors are the Austrian national bank, which has refused, a supermarket chain, which has yet to reply, and the businessman and former vice-chancellor Hannes Androsch, who said he "did not exclude" a contribution.
Article published with permission from the European Jewish Press , a pan-European news agency based in Belgium