Professor Petrovsky-Shtern said the performance was consistent with a “cynicism that pervades Russian politics” from the top down.

Deborah E. Lipstadt, a professor at Emory University and a scholar of the Holocaust, asked on Twitter: “Have you lost all sense of decency? Have you no shame?”

Others, like the American comedian Sarah Silverman and the British writer and lawyer Rupert Myers, also took to social media to express astonishment and dismay.

Ms. Navka, who is married to President Vladimir V. Putin’s chief spokesman, Dmitry S. Peskov, won a gold medal for Russia in ice-dancing at the 2006 Winter Olympics in Turin, Italy, with Roman Kostomarov.

Ms. Navka and Mr. Burkovsky danced to the signature song from “Life Is Beautiful.” It was performed by the Israeli singer Achinoam Nini, known by her stage name, Noa, and the dance was choreographed by Ilya Averbukh, a Russian ice dancer and former Olympic medalist, who is Jewish.

The film, directed by Roberto Benigni, about a man who seeks to protect his son by convincing him that the Nazi persecution they were experiencing was part of an elaborate game, was nominated for the 1999 Academy Award for Best Picture and won the Oscar for best foreign-language film. Mr. Benigni, who also starred in the film, won best actor. Some have criticized the film, however, for sentimentalizing one of the darkest events in history.

In a post on Instagram, Ms. Navka suggested that the dance routine had intended to draw attention to the film.