Police in Troitskoye village said they found the bodies of the woman's 3-year-old daughter and 5-year-old son Monday.
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 RIA Novosti news agency said the 24-year-old woman, whose name had not been released, survived the suicide attempt.
A similar incident occurred in June near Moscow when Galina Ryabkova killed her two sons by throwing them off a 15th-floor balcony.
Ryabkova was later declared insane and committed to a psychiatric clinic for treatment, RIA Novosti said.