An arbitration court has ordered Austria return the five Klimt paintings seized during Nazi rule to Maria Altmann, heir of their Jewish former owner who fled the country under the Nazis.
The paintings valued at more than 100 million euros ($A161 million), include one of Klimt's most iconic paintings, Adele Bloch-Bauer I, a portrait of the original owner's wife surrounded by gold, and a second portrait of her.
"I would also like the portraits to remain in Austria," Altmann told Austrian state television, adding she wanted the landscapes to remain in museums.
The paintings were seized by the Nazis when Germany annexed Austria in 1938 and were put on display in Austria's Belvedere Gallery after World War II, where they are still kept today.
Austrian culture minister Elisabeth Gehrer said, however, that Austria could not afford to buy back the paintings.
Media reports claim that Adele Bloch-Bauer I, also called the 'Golden Adele', alone was worth between 70 million ($A112.71 million) and 100 million euros ($A161 million).
"70 million euros amounts to the whole budget for all (public) museums in Austria," said Ms Gehrer adding that the government would comply with the ruling and hand over the paintings.
"That means we are not financially able to make purchases here, but talks will be held. Perhaps there are sponsors or the family itself is prepared to make something available as a loan," said Ms Gehrer.
Ms Altmann, the 89 year old niece of the paintings' owner, Czech sugar magnate, Ferdinand Bloch-Bauer, sued Austria in 1999.
She and the Austrian government agreed to observe the ruling of an arbitration court in Vienna, which found in her favour.
When Bloch-Bauer's wife Adele died in 1925, she left a will requesting her husband leave the artwork to the Austrian gallery upon his death.
Ferdinand Bloch-Bauer fled Vienna to Switzerland, where he died in 1945.
In his will, he left everything to his nephew and nieces, including Altmann.
But his family agreed in 1946 the paintings belonged to the Austrian government, based on his wife's will.
Altmann, who fled to California to escape the Nazis and is Ferdinand Bloch-Bauer's sole surviving heir, said the family was extorted into signing away its rights to the paintings in 1946 and had been lied to by the Austrian government.
Klimt paintings of an importance similar to the Adele portraits are rarely sold in art auctions.
In 2003, a landscape showing a country house on the Attersee in Austria, changed hands for $US26 million ($A34.49 million) at Sotheby's in New York.