The bodies of a three-year-old girl and a five-year-old boy were discovered by police in Troitskoye village in Kalmykia region.
Police said the killings may be linked to a recent court verdict in which the woman's husband was found not guilty of sexually abusing one of her children.
Police said the 24-year old woman survived her suicide attempt and that medics were fighting to save her life.
The case mirrors an incident in June, when a resident in the Moscow region town of Dolgoprudny killed her two small sons by throwing them from a balcony on the 15th floor.
The woman, Galina Ryabkova, was declared insane and committed to a psychiatric clinic for treatment.