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.
Even before his death, in such a state, he never lost his human dignity
Walter Litvinenko
Litvinenko obituary Denials fail to solve mystery
"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".
Mr Litvinenko's condition deteriorated rapidly in hospital
Litvinenko statement
"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.
Mr Alexander Litvinenko, reputed to have been an Ex-Russian spy who had defected to Britain, died last night in mysterious circumstances. He had alleged many associations between people in high places and organised international crime, implying that President Putin and Romano Prodi among others had been involved personally. He had sought political asylum in UK in 2000 and became a naturalised citizen in October this year, just weeks before his death.

Mr Litvinenko was said to have been investigating the shooting of Russian journalist and human rights activist Anna Politkovskaya, a well-known critic of Russian activities in , in her apartment in Moscow October 7, 2006. It is reported that he had met two Russians in a hotel room, one said to be former member of the  in connection with the affair and he went on to meet Mario Scaramella at a  bar in Piccadilly where some papers were exchanged. Some hours after this he was taken ill. 

Mr Litvinenko was admitted to , north London on November 1, 2006 complaining of feeling sick. By November 11, he was said to be suffering from ''serious poisoning''. A week later he was transferred to  in central London. A week later he was said to have been poisoned by ingesting , once used in rat poison, but, in the opinion of some doctors, there were signs of , including loss of weight and shedding of hair. Various explanations of his condition were offered. Last night he suffered a heart attack, after having left a message blaming President Putin for having him killed. 

The radioactive  -210 was found in his blood and urine as reported by the . The post-mortem was cancelled. Subsequently the Agency examined conditions in the hospitals in which Mr Litvinenko has been treated. Police visited the Itsu sushi restaurant in Piccadilly, his home in Muswell Hill and the Millennium Hotel, Grosvenor Square where the meeting on November 1 had been held. Traces of radiocactivity were found in all three places. It is speculated that the polonium was probably eaten by Litvinenko as a substance that could be combined with a salt-like substance, such as .

It was reported that a meeting had been held in Cabinet Office Briefing Room A (COBRA) used for high level emergency planning and control, to consider the implications of these events. The Foreign Office asked Moscow for a response to the accusation of Russian involvement and President Putin himself dismissed the allegations saying (before the cause of death had been established) that there was no proof of an unnatural death and that the case was being used as a "political provocation".