He is ready to anoint Vyacheslav Volodin, the speaker of the Russian parliament, as his chosen successor as president, it is suggested, but there are fears the text could be a dirty trick involving warring rivals close to the powerful leader.
President Putin was evidently caught by surprise when confronted with the claim at a public Kremlin session.
He paused before giving an answer that neither confirmed nor denied whether he will fight next year's presidential election.
Klintsevich calls Volodin the successor to the President of the Russian Federation
Most pundits predict the strongman to seek another six years in the Kremlin, and few doubt he would win by a landslide, but he has not so far announced he will stand again.
Speaker Volodin – a devout loyalist with a high public profile who served previously as his deputy chief of staff – has not yet commented on the swirling rumours, but in December publicly urged President Putin to stand for another term.
The letter alleging Speaker Volodin "would soon be president" was supposedly penned by another Putin political friend Frants Klintsevich, a senior senator, who is close to both men.
Russian president Vladimir Putin is ready to quit, according to a new letter
Klintsevich later claimed the letter was a "fake", and he is known to be embroiled in an ugly dispute the man who evidently shocked President Putin by reading it out, Andrey Chepurnoy, the leader of a group of Afghan War veterans.
"The most outrageous thing, Vladimir Vladimirovich [Putin], is that here, in this very letter, Klintsevich calls Volodin the successor to the President of the Russian Federation," Chepurnoy told him.
"Vladimir Putin paused to cope with the information he had just received," reported newspaper Moskovsky Komsomolets.
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"It's not every day that someone confronts him with the name of his successor – and right before the presidential election."
He replied testily with no clue as to any truth that Speaker Volodin is his chosen heir: "The president's successor will be determined only by the Russian people during a democratic election – and nobody else can do it."
Speaker Volodin, 53, a lawyer before entering politics, was seen with "a completely stony faced expression" after Chepurnoy's outburst, said a witness.
An ally of the speaker, Sergey Neverov, gave an interview in which he repeatedly avoided answering whether he wanted Speaker Volodin as president.
Yet nor did he back President Putin for another term.
According to the letter President Putin is ready to anoint Vyacheslav Volodin
Klintsevich claimed the letter was "fake" and was made up to some "ugly purpose".
"Any graphology expert will prove my words" he said, although the text appeared to be typed.
One theory was that rivals for President Putin's job may have wanted to embarrass Volodin by labelling him as the heir.
Chepurnoy raised the letter in a public session with Putin as part of a battle between him and Klintsevich who has claimed the Afghan War veterans organisation is not run transparently.
"He is calling the regions and scares our members, leaders and officials, saying that Volodin would soon be a president, and that he will grant Klintsevich enormous privileges," he said.
Putin has neither confirmed nor denied whether he will fight next year's presidential election
Klintsevich would then "bury alive" the leadership of the organisation which has rehabilitated 100,000 patients, he said.
President Putin vowed to look into the allegations – "we'll deal with it" – but did not address who would be ruling party United Russia's candidate in next year's election.
The Russian president has indicated he yearns to travel without the weight of high office, yet he has created a system which could lurch into bitter infighting without him as lynchpin.
In December, Speaker Volodin showed urged Putin – who has been president or prime minister since 1999 – to announce he would seek another term.
"We have a candidate," said Volodin.
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"And we will keep supporting him.
"You know him – and I think you will support him too.
"Because he is a man who has proved with his labour and his service that he can do a lot for Russia, that he loves it.
"He is doing everything for our country and he is acknowledged in the whole world."
If he completes a final term, President Putin would be 71 before retiring.