Called the Guelph Treasure or "Welfenschatz", it includes gold and silver relics, gem-studded crucifixes and other ornate Christian artefacts, some dating back to the 11th century and believed to be worth hundreds of millions of euros.
The fight centres on whether its three Jewish former owners sold the collection under duress and below market price in a deal with the Prussian state in 1935, two years after Nazi dictator Adolf Hitler rose to power.
The case comes when Germans are being accused of foot-dragging on the return of Nazi-looted art to their rightful owners following the discovery of a vast trove of long-lost artworks found in a Munich flat.
Germany's government-backed Limbach Commission which reviews such cases, with a former state president, top court judge and historian among its eight members, started hearing the dispute Wednesday, said a spokeswoman.
Later in the day she told AFP the closed meeting had ended and that "the discussions are ongoing and a recommendation is expected in coming weeks". The findings are non-binding but are seen to carry significant moral weight.
In the years-old dispute on the now 42-piece collection - the largest German church treasure in public hands - the heirs claim that the art dealers had no choice but to sell it to the Nazi state below value.
The syndicate of Frankfurt art dealers had bought the collection in 1929 but saw its value drop sharply as the market collapsed in the Great Depression.
Having sold off about half of the pieces, they parted with the remaining objects in the 1935 sale to the state of Prussia, then led by Hermann Goering, the Gestapo secret police founder and air force chief.
The Prussian Cultural Heritage Foundation, which oversees the Berlin museum now holding the treasure, says the dealers received "a fair and appropriate price".
"Although the sellers were Jewish citizens, some of whom were resident in Germany at the time of the sale and some of whom lived abroad, the sale of the Welfenschatz was not a forced sale resulting from Nazi persecution," it said in an online statement.
It also pointed out that at the time of the sale, the collection was in storage in Amsterdam and not under "the authority of the German state".
Markus Stötzel, a lawyer for the Jewish families, has stressed that "all the participating art dealers and their relatives lost their personal and professional existence in Germany due to racial persecution".