Litvinenko, a former FSB agent, died in London last year after being poisoned with polonium-210, a highly radioactive isotope.
The FSB statement did not state that the investigation related to the death of Litvinenko, and did not name any suspects.
However, it appeared to refer to "material" that Lugovoi said at a news conference last month he will soon present to Russian security services.
Russia has repeatedly refused to hand over Lugovoi to Britain.
Lugovoi denies involvement in the killing and alleges that it was carried out either by Britain's MI6 intelligence agency, the Russian mafia, or Boris Berezovsky, a former Russian agent who is now an exiled opponent of the Kremlin.
He has suggested that Berezovsky and Litvinenko were working for MI6.
"It is hard to escape the thought that Litvinenko had become an agent who had escaped the control of the special services and they took him out," Lugovoi said in May.
British suspicion fell on Lugovoi and an associate, Dmitry Kovtun, after it emerged that both met Litvinenko in a London hotel on November 1, the day he fell ill.
The men left traces of the radioactive isotope used in Litvinenko's killing in various locations as they returned to Russia.