The dancers wore black-and-white striped outfits with numbers and yellow stars for the routine, which ends to the sound of gunfire
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 89,000 times by Monday afternoon, 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".
Israel's Russian-language newspaper Vesty Israel wrote on Facebook that it hoped choreographer, ice dancer Ilya Averbukh, "has enough brains not to bring this routine to Israel."
Averbukh -- who is reportedly of Jewish origin -- angrily defended the routine to Komsomolskaya Pravda tabloid, saying, "I would call all this reaction a sign of the craziness of today."
Navka herself insisted that the camp prisoner uniform was simply part of the performance, telling Life News website: "This is our job."
She said the global reaction "means we are forcing people to think."
Asked to comment on the furore, Peskov told journalists: "I am proud of my wife, that's all I can say."
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 said in an interview with Govorit Moskva radio station that 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."
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.
The weekend show was not the first time ice dancers have tackled the risky topic of the Holocaust.
In the Sochi Winter Olympics in 2014, Russian teen figure skater Yulia Lipnitskaya danced a routine, also choreographed by Averbukh, set to the music of Steven Spielberg's "Schindler's List".
Lipnitskaya wore a red costume echoing a victim's red coat in the film in a performance that prompted a standing ovation from Putin but also some accusations of tastelessness.