Litvinenko, a Kremlin critic, died from radioactive poisoning in London in late November.
British detectives traveled to Moscow in December as part of the probe into his killing and Scotland Yard today said there were no definitive plans for them to return to Russia.
Chaika said his office wants to question fugitive Russian tycoon Boris Berezovsky as part of Russia's own investigation into Litvinenko's death.
Berezovsky, a strong Kremlin critic, lives in Britain, where he was granted political asylum.
Chaika said that as part of the Litvinenko probe, prosecutors were also seeking to question Leonid Nevzlin, a former shareholder of the bankrupt Yukos oil company who fled to Israel.
(Interfax, AFP, AP)