Germany's representative before the International Court of Justice, Susanne Wasum-Rainer stated, "We are here to obtain a ruling by the court on legal issues of great significance, not only to both parties... but also international law."
Germany lodged its application before the ICJ in December 2008, saying that by permitting claims for abuses which happened between September 1943 and May 1945, Italy "failed to respect the jurisdictional immunity" that modern-day Germany enjoys under international law.
It is asking the ICJ to order Italy to take steps to ensure decisions by Italian courts "infringing on German sovereign immunity" cannot be enforced.
Third Reich troops committed war crimes after Italy switched sides to the Allies in September 1943, including in the case of Luigi Ferrini, who was deported to Germany as a forced labourer in August 1944, court documents said.
Ferrini claimed compensation from Germany in 1998 and since an Italian Supreme Court decision in 2004 in his favour; hundreds of other claims by relatives and widows of victims of Nazi war crimes have been brought before Italian courts.
The courts in turn have argued that the cases were admissible because abuses committed by German troops amounted to "international crimes" which took precedence over state immunity.
"Only an authoritative finding will lead out of the impasse and will clarify this complex legal issue," Wasum-Rainer told a 16-judge bench of the Hague-based court.
Also before ICJ is Greece, because relatives of victims of a 1944 German massacre of Greeks at Distomo, in Greece, which claimed 218 lives, turned to the Italian courts after their case stalled in Athens.
"We are here because we want to find our right to justice. We hope for a positive outcome for Italy. Germany must respect the decisions taken in Italian courts," a representative of Distomo victims told AFP outside the court.
Greece however is taking part in the hearing as a non-party state.