Litvinenko, a Kremlin critic who was granted asylum in Britain, died in London in November 2006 from radioactive poisoning.
Lugovoi, a former Russian security agent, had met with Litvinenko on the day Litvinenko fell ill but has denied any involvement in his death.
Russian officials have said Lugovoi will not be handed over, saying Russia's Constitution prohibits the extradition of its citizens.
On his deathbed, Litvinenko accused Russian President Vladimir Putin of being behind his poisoning. The Kremlin denies any involvement.
The case has added tension to Russia's relations with Britain.
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