President Vladimir Putin has said the death in London of ex-Russian spy Alexander Litvinenko is being used as a "political provocation" against Russia.
Speaking before UK police said they had found radioactive material in his body, Mr Putin said there was no evidence Mr Litvinenko's death had been unnatural.
Friends of Mr Litvinenko believe he was poisoned by Russian government agents.
In a statement made before his death, Mr Litvinenko accused the Russian leader himself of involvement.
Kremlin officials have dismissed such allegations as "sheer nonsense".
Mr Litvinenko's death has been linked to the presence of a "major dose" of radioactive polonium-210 in his body. British authorities are investigating how it got there.
The dead man's friends have alleged he was poisoned because of his criticism of Russia.
Mr Litvinenko was granted asylum in the UK in 2000 after complaining of persecution in Russia.
'Howl of protest'
"The death of a person is always a tragedy. And I convey my condolences to those close to Mr Litvinenko, to his family," Mr Putin told a news conference in the Finnish capital Helsinki, where he is attending a summit with the EU.
"Meanwhile, as far as I know, in the medical report of British doctors, there is no indication that this was an unnatural death. There is none. That means, there is no reason for discussion of that kind.
"I hope that the British authorities will not encourage political scandals that do not have real grounds to be blown up, whatever they are."
The accusation against Mr Putin came in a "message to the person responsible for my present condition" read out by Mr Litvinenko's friend Alex Goldfarb.
It was dictated on 21 November, when Mr Litvinenko realised he could die.
"You may succeed in silencing me, but that silence comes at a price," the statement said.
"You have shown yourself to be as barbaric and ruthless as your most hostile critics have claimed.
"The howl of protest from around the world will reverberate Mr Putin in your ears for the rest of your life," the statement added.
'Tiny nuclear bomb'
After Mr Goldfarb had read out the statement, Mr Litvinenko's elderly father, Walter - who flew to the UK from Russia this week - said his son had been killed by a "tiny nuclear bomb".
"It was an excruciating death, he was taking it as a real man," he said.
"Even before his death, in such a state, he never lost his human dignity."
Mr Litvinenko was a fierce critic of Mr Putin. He alleged that the Russian authorities were responsible for bombings in Moscow seven years ago that killed 200 civilians. The attacks were blamed on Chechen rebels and led to the second Chechen war.
He had also recently been investigating the murder of another Putin critic, outspoken Russian journalist Anna Politkovskaya.
Mr Litvinenko died in a London hospital on Thursday - more than three weeks after falling ill.