Interfax quotes prosecutors as saying they will also investigate what they said was the attempted murder of Dmitry Kovtun, who met with Litvinenko in a London hotel on November 1, the day Litvinenko fell fatally ill.
British investigators are currently in Moscow conducting an investigation of the Litvinenko murder in Moscow.
Meanwhile, in London, Britain's Health Protection Agency says seven workers at a London hotel where Litvinenko met a contact have tested positive for polonium-210, the adioactive isotope that toxicologists found in Litvinenko's body. The health agency said the hotel's employees had been exposed to low levels of radiation and that there was no risk to their health in the short term.
Russia's decision to open its own investigation would allow suspects to be prosecuted in Russia. Earlier this week, Russia's chief prosecutor said no possible Russian suspects would be extradited in connection with the probe.
Russian prosecutors will also look into what they describe as the attempted assassination of an associate of Litvinenko, Dmitry Kovtun, who they say is also suffering from radiation poisoning.
Friends today held a memorial service for Litvinenko at a mosque in central London. Litvinenko, who had reportedly converted to Islam shortly before his death, was expected to be buried later today.