Prominent lawyer and art patron Peter Raue, who works closely with museums in Berlin, said Germany must do its part for transparency as many families of Jews stripped of their assets under the Nazis believe their works may be among those found.
"It would be more sensible to post the paintings on the Internet, why not with the (London-based) Lost Art Register?" he told the daily Tagesspiegel.
"Only then can there be a chance, for example, for the owners of the breathtakingly beautiful suspected Matisse painting presented Tuesday to come forward. Maybe the Winterstein family from Ohio will say: that picture was hanging in our home in Berlin on Klopstockstrasse."
Despite international pressure, German prosecutors have refused to publish a full inventory of the works, citing a need for more time to fully catalogue them and for discretion in their probe.
They have launched an investigation on charges of tax evasion and misappropriation of assets against Cornelius Gurlitt, in whose garbage-strewn Munich apartment the more than 1,400 works including paintings by Pablo Picasso, Pierre-Auguste Renoir and Henri Matisse were found in February 2012.
The case only came to light this week in a magazine report. Gurlitt is the son of Hildebrand Gurlitt, a powerful Nazi-era art dealer and collector who acquired the paintings in the 1930s and 1940s.
Hildebrand Gurlitt had been tasked by the Nazis with selling works looted from Jewish collectors or seized as part of a crackdown on avant-garde, so-called degenerate art in exchange for hard currency.
However he appears to have held on to many of the works, even after an investigation by US occupying forces after the war, and he left them to his family after he died in a car accident in 1956.
The federal cultural ministry said it was in talks with the Bavarian state government about speeding up the research and publishing the names of paintings "as soon as the provenance of a work is unclear", a spokesman told German news agency DPA.
Chancellor Angela Merkel's spokesman Steffen Seibert also called for openness, while stressing that the prosecutors were responsible for the probe.
"The federal government is pushing with urgency, independent of the criminal inquiry, for information on confiscated artworks to be published for which there is already evidence that they were seized as part of Nazi persecution," he told reporters Wednesday.
Meanwhile, based on slides of a few of the modernist masterpieces in the collection shown at a news conference Tuesday, several museums said they were researching whether works had been among their holdings.
Ulrike Lorenz, the director of the Kunsthalle Mannheim in southwestern Germany, told public radio that it may have held the portrait "Melancholy Girl" by Ernst Ludwig Kirchner which was seized by the Nazis in 1937 and considered missing ever since.
The Von der Heydt Museum in the western city of Wuppertal and the Folkwang Museum in Essen also said they had grounds to believe some of their previous "degenerate art" holdings were part of the Munich stash.
They noted, however, that because the Nazis changed the law to allow them to pillage museum assets, their legal claim to paintings may well be weaker than that of Jewish heirs whose works were looted.
Cornelius Gorlitt's mother Helene had claimed years after the war that their entire collection and all records were destroyed in the 1945 bombing of Dresden, according to a letter that recently surfaced.
However the Holocaust Art Restitution Project (HARP) posted a document on its Facebook page of artworks seized from Hildebrand Gurlitt by US troops immediately after World War II that were returned to him in 1950 after intensive lobbying.
He reportedly assured the Americans that the works had not belonged to Jews.
HARP in a statement called on European neighbours to turn up the heat on the German authorities.
"The governments of France, Belgium, and Holland have a legal and moral responsibility to demand immediately from the German government that it release the list of all items found in the possession of Cornelius Gurlitt," it said.
READ MORE: Masterpieces emerge from Nazi art trove