Germany's best-selling tabloid Bild and its Berlin affiliate B.Z. had urged readers to send letters of protest to parliament to demand the removal of the tanks.
Chancellor Angela Merkel's deputy spokesman Georg Streiter quashed the bid on April 16.
Streiter noted that Germany signed a treaty with Russia in 1990 pledging to "respect, maintain and care for" the Soviet war monuments in their current form.
The Soviet war memorial is dedicated to the 80,000 Red Army soldiers killed during the Battle of Berlin in the spring of 1945. It features columns, a giant statue of a Russian soldier, and two T-34 tanks.