"The results will not be known soon, definitely not on Friday," he said.
Alexander Litvinenko, a former Federal Security Service officer and outspoken Kremlin critic with ties to exiled Russian oligarch Boris Berezovsky, died November 23 in a London hospital from a lethal dose of radioactive polonium-210.
Lugovoi is currently in hospital in Moscow.
Lugovoi and another witness Dmitry Kovtun, both businessmen and former security agents, met with Litvinenko around the time he fell ill, and have already been questioned by Russian and British investigators probing the Litvinenko case.
Kovtun, diagnosed with radioactive poisoning by doctors in Moscow, told RIA Novosti Thursday that he will not be discharged from hospital soon.
"It may take several weeks," he said.
He also denied western media reports that he visited Berlin recently. "This is easy to check," he said.
A German newspaper said earlier on Thursday, citing law enforcement sources, that Kovtun made a phone call to his former mother-in-law, living in Hamburg, on December 12 from Berlin.
Police confirmed that that the signal came from Berlin, but called it a false trail.
Police in Hamburg launched an investigation into Kovtun after traces of radiation were detected at several sites he visited between October 28 and November 1, including at his ex-wife's apartment. German prosecutors are investigating the businessman, who has a German residence permit, on suspicion of illegally transporting nuclear materials.