Germany urged the ICJ to overturn an Italian court's decision that Berlin pay compensation to the families of the victims of the Arezzo massacre, when Nazi troops killed 203 men, women and children in the central province of Tuscany on June 29, 1944.
"With its judicial practice Italy broke its obligations to Germany in accordance with international rights and it continues to break them," Germany said, adding that the ruling contravenes the country's "sovereign immunity."
The ruling from Italy's highest appeal court in September was the first time an Italian court had ordered Germany to pay compensation in a criminal case.
The families of nine of the Arezzo victims asked for and were awarded a total of €800,000 ($1.05 million) in damages from the military court in September 2007.
A lawyer acting for the German government argued before the Italian court that previous agreements between the two countries had put an end to this type of case.
Based in The Hague, the ICJ is the United Nations' main judicial body. It was set up in 1945 and began its work the following year