By Agence France-Presse
Tatiana Navka, an Olympic ice dancing champion who is married to Kremlin spokesman Dmitry Peskov, performed the pirouetting routine with actor Andrei Burkovsky on a prime-time celebrity skating show on Saturday.
The dancers wore black-and-white striped outfits with numbers and yellow stars for the routine, which ends to the sound of gunfire.
The routine was set to a song from 1997 Oscar-winning Italian film "Life is Beautiful," a tragicomedy about a father trying to hide the horrors of concentration camp life from his son.
The pair won maximum points on the Ice Age show on state-controlled Channel One and praise from judges, while Navka wrote on Instagram that it was one of her "favourite routines", and "our children should know and remember this terrible time."
The routine prompted a wave of discussion online and in international media.
"Have you gone mad? Smiles in prison uniforms with yellow stars! The audience erupting in applause... No taste, no, tact, no understanding," wrote viewer Mihael Ratinsky on the Channel One website.
"This is terrible, people don't understand what they are doing. This is blasphemy," wrote another viewer, Viki Reznik, in a comment to a YouTube video that had been viewed more than 36,000 times on Monday, with most reactions negative.
Britain's the Daily Mail wrote that the dancers' "beaming grins" seemed to have "little in connection with their gruesome theme," while US People magazine's site called it "troubling."
The Nazis killed some 10 million Soviet civilians and prisoners of war, some 1.3 million of whom were Jewish, according to the US Holocaust Memorial Museum.
Head of the Moscow-based Holocaust Fund Alla Gerber told interview with Govorit Moskva radio station it was "very complex" to depict the Holocaust appropriately.
"Primarily I think there must not be mockery, there must not be irony, there must not be a crooked smile."
Russian ice dancer Ilya Averbukh, who choreographed the routine, angrily defended it to Komsomolskaya Pravda tabloid on Monday, saying "I would call all this reaction a sign of the craziness of today."
Navka was already a popular star and television personality before marrying Peskov in a swanky ceremony on the Black Sea coast last year, but their marriage has made them one of Russia's most-watched celebrity couples.