Litvinenko died last week of radioactive poisoning, putting a strain on British-Russian ties.
Blair, who could meet with Russian President Vladimir Putin at a NATO summit in Riga, said there will be "no diplomatic or political barrier in the way of [the police] investigation going wherever it needs to go."
Litvinenko blamed Putin for his death in a statement read out by his friends after his death.
The Kremlin has denied any involvement, and Russian prosecutors have offered to help with the investigation.
(dpa)