Litvinenko, who died last month in London, had blamed President Vladimir Putin for his death, an accusation the Kremlin has denied.
Earlier this week, Lavrov said insinuations of high-level Russian involvement could damage ties.
British authorities are treating Litvinenko's death as murder, but say they do not yet know the manner, the motive, or who might be responsible.
British investigators are currently in Moscow questioning possible witnesses.
Litvinenko is scheduled to be buried today in London. Aleksandr Goldfarb, a close associate, said Litvinenko would be buried in a private nonreligious ceremony.
Previous reports said Litvinenko, who reportedly converted to Islam before his death, would be buried according to Muslim tradition.
(compiled from agency reports)