Nadezhda Tolokonnikova, 22, and Maria Alyokhina, 24, petitioned to stay out of prison until their children reach the age of 14, the Russian news agency RIA Novosti reported.
The women are scheduled to be sent to a penal colony hundreds of miles from Moscow after their request to remain at the pretrial detention center was turned down.
A hearing date for their deferral of sentence petition will be held within 10 days, said lawyer Mark Feigin.
The women were sentenced to jail in August after a court found them guilty of "hooliganism with the aim of inciting religious hatred."
Notable deaths of 2014 [PHOTOS]