Lugovoi, also a former Russian security officer, met with Litvinenko at a London hotel on November 1, the day Litvinenko fell ill.
Litvinenko died on November 23 of poisoning from the rare radioactive isotope polonium-210.
Britain is investigating the case as murder.
Russia last week opened its own probe into the death of Litvinenko.
According to Interfax, Russian detectives could travel to Britain by the end of the week to gather evidence on the case.
Meanwhile, German police say four people have been found to be contaminated with polonium-210.
The four include the ex-wife of businessman Dmitry Kovtun, her current partner, and their two children.
Kovtun met Litvinenko in London on the same day as Lugovoi.
(compiled from agency reports)
CLOAK AND DAGGER: A timeline of a murder case that unraveled after Andrei Litvinenko, a former Russian security officer and vocal Kremlin critic, dies on November 23, 2006, of poisoning by radioactive isotope polonium-210.
In a deathbed letter, Litvinenko blames Russian President Vladimir Putin for his death -- a claim Putin condemns.
Investigators center on two meetings in London that Litvinenko had described -- one in which he met with two Russians for tea in London, and another in which he met with a third Russian at a sushi bar.
Six months later, British prosecutors announce they have enough evidence to charge a Russian citizen -- one of the men who had met with Litvinenko for tea -- with the murder ...more...
MORE: Coverage in Russian from RFE/RL's Russian Service.