British detectives in Moscow and Russian investigators interviewed Kovtun on Wednesday who, with Andrei Lugovoy, a businessman and ex-KGB spy, met Litvinenko in a London hotel on November 1.
Lugovoy is also undergoing treatment in Moscow for radiation contamination.
On Thursday, Russian prosecutors simultaneously announced investigations into the Kovtun poisoning and the murder of Litvinenko.
The announcement came as Litvinenko was buried in London. He died after exposure to polonium-210, a radioactive isotope.
A Russian prosecution statement said: "The Russian prosecutor-general has opened a criminal case in connection with the murder of Russian citizen Alexander Litvinenko and the attempted murder of Russian citizen Dmitry Kovtun."
British police are treating Litvinenko's death as a murder inquiry.
In a statement released after his death, Litvinenko accused Vladimir Putin, the Russian president, of killing him. The Kremlin has denied involvement.
Litvinenko was buried at London's Highgate cemetery.
Mourners included emigre Russian billionaire Boris Berezovsky, a Putin critic and Litvinenko associate, and Akhmed Zakayev, the London envoy for the Chechen separatist insurgency with whom Litvinenko had worked.
Zakayev and Litvinenko's father, Walter, had earlier said prayers for him at the Regent's Park Mosque in central London.
Zakayev has said Litvinenko converted to Islam before his death though another associate said he was unaware of any conversion.
Also on Thursday, a British health agency said that seven staff from a London hotel bar where Litvinenko drank before his death have tested positive for traces of polonium-210, the same radioactive isotope which killed Litvinenko.