Count Jaromir Czernin had sold Flemish painter Johannes Vermeer's masterpiece to the Nazi dictator "to protect the life of his family", his descendants' attorney, Andreas Theiss, told Der Standard.
Czernin's wife was of Jewish origin and he was also the son-in-law of Austrian leader Kurt von Schuschnigg, who was toppled by the Nazis.
Hitler acquired the painting for 1.65 million Reichsmarks, Der Standard said.
But the family's attorney said a new expert appraisal found that the painting was sold for no more than one million Reichsmarks, or "a fraction of its value".
"The Art of Painting," which Vermeer created in 1665, has been on the walls of Vienna's Kunsthistorisches Museum since 1946. It is the Flemish master's largest painting.
"We are convinced that the Austrain republic will treat this case in an open and honest manner," Theiss said, adding that he had filed the request on August 31.
The culture ministry confirmed Saturday that it had received Theiss's request and would transmit it to a committee tasked with issuing opinions on restitutions.
The painting has been owned by the Czernin family since the 19th century.
The family had already asked for the painting to be returned in the 1960s, but their requests were rejected on the basis that it had been sold voluntarily and at an appropriate price.
Jaromir Czernin had tried to sell the painting in 1938 for one million dollars to an American collector, but his plan was thwarted by the German invasion of Austria and Hitler's opposition, Theiss said.
Hitler had expressed interest in acquiring the painting as early as 1935 to put it in the Fuehrer Museum which he planned to build in the Austrian city of Linz.http://www.google.com/hostednews/afp/article/ALeqM5hnCbbnXJ6MLfU8u4JKC22dH37zjA