The 50-second video, displayed on public transportation in Athens, features graphic images of wartime suffering, including people starving to death, children being sent to concentration camps, and villages being destroyed. The video's tagline is: "We claim what Germany owes to us."
"The focus (of the campaign) is to rescue the historical memory of the Greek people," said Kyriakos Zilakos, a Greek Defense Ministry spokesman.
Athens claims Germany owes Greece 279 billion euros ($317 billion) in reparations for war damages. Berlin has firmly rejected the claim and said the matter has long been closed. Germany paid Greece 115 million marks in 1960, as required by reparation agreements. On top of that, it also paid compensation directly to individual victims of the Nazi regime in Greece -- forced laborers, for example.
But the Greek government is now saying the past payments were not enough.
"The issue of German debt is above all an ethical issue and the whole campaign aims at closing the wounds of the past," Zilakos said.
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German war debt to Greece has been raised many times before -- most recently in 2010 and 2012, when Greece was negotiating the terms of its 240 billion euros ($260 billion) international bailout package.
The relationship between Athens and Berlin has been deteriorating rapidly since the new Greek government started accusing Germany and its other creditors of bullying.
But Athens said the latest campaign is not meant as an attack on Germany. "The video is in no way directed against the German people," Zilakos said.
The campaign will run for a month with the spot being shown on screens in the Athens subway and suburban railway stations, he said. It will be shown in other locations in Greece as well.
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CNNMoney (London) May 14, 2015: 1:28 PM ET