Russia says the D-Day invasion "did not have a decisive impact" on World War II and its significance "should not be exaggerated".
Maria Zakhorova, a spokeswoman for Russia's ministry of foreign affairs, spoke as ceremonies were taking place to mark its 75th anniversary.
"It should of course not be exaggerated," she said. "And especially not at the same time as diminishing the Soviet Union's titanic efforts, without which this victory simply would not have happened."
The Soviet Union lost over 25 million lives in what it calls the Great Patriotic War, and Moscow under President Vladimir Putin has taken to marking victory in the war with a massive annual military parade on Red Square.
"As historians note, the Normandy landing did not have a decisive impact on the outcome of World War Two and the Great Patriotic War.
"It had already been pre-determined as a result of the Red Army's victories, mainly at Stalingrad (in late 1942) and Kursk (in mid-1943)," Zakharova told reporters.
Zakhavora's words did include a tribute to those who lost their lives on the Western Front and said Moscow appreciated the effort.
The D-Day invasion was the largest seaborne invasion in history that was the beginning of the end of Nazi Germany's occupation of western Europe.
Moscow, which had been fighting German forces in the east for almost three years by the time of D-Day, and gradually pushing them back from early 1943, had been urging Britain's Winston Churchill to open a second front as far back as August 1942.
Zakhorova's statement follows an article written by Sergey Lavrov, Russia's foreign minister, in Russia's International Affairs magazine. Lavrov said that the D-Day operations are part of "pseudo-historical theories" introduced to the "Western education system" that "belittle" the efforts of the Soviet Union during World War II.
The Russian Embassy in the US has also issued a number of tweets highlighting the role of the Soviet Union's Red Army during WW2 and state that "the brunt of the war against Nazism" was still "primarily carried by the USSR".