Putin told a reporter from Kommersant newspaper that Wagner, which staged a brief armed mutiny last month, "does not exist" in a legal sense because there is no law in Russia relating to private military companies.
Kremlin spokesman Dmitry Peskov told reporters that the status of companies such as Wagner was "rather complicated" and needed to be studied.
Asked if new legislation was likely on the status of private military companies, he said: "This question will at least be under consideration."
Wagner has waged the fiercest battles of the Ukraine war for Russia but uncertainty has surrounded its fate and that of its leader Yevgeny Prigozhin since last month's mutiny, when it seized control of a southern city and advanced towards Moscow.
The defence ministry said this week that Wagner was completing the transfer of its weapons to the regular army under the accord with the Kremlin that brought the mutiny to an end.
Putin told Kommersant that he had offered Wagner mercenaries the opportunity to keep fighting for Russia during a meeting held five days after the mutiny but suggested Prigozhin be moved aside in favour of a different commander.
Putin told the newspaper that one option would see Wagner keep the same commander who goes by the call name "Grey Hair" and has led the private army in Ukraine for 16 months.
"All of them could have gathered in one place and continued to serve and nothing would have changed for them. They would have been led by the same person who had been their real commander all along," he said.
Putin said many Wagner troops nodded in approval at the proposal, but Prigozhin, who was sitting in front and didn't see their reaction, quickly rejected the idea, responding that "the boys won't agree with such a decision."
Under the terms of the agreement ending the June 23-24 mutiny, Prigozhin was meant to go into exile in Belarus, a close ally of Russia. However, he has not been seen in public since June 24 and his current whereabouts are unknown.
Prigozhin had called Russian military leadership corrupt and incompetent, and had complained for months of inadequate munitions supplies.
Putin described the revolt as "treason" at the time.
Shortly before his troops reached Moscow, Prigozhin ordered a retreat after negotiations with the Kremlin, in which Belarusian President Alexander Lukashenko acted as mediator.
On Friday, the Belarusian government said soldiers with Wagner had arrived in the country from Russia and are training Belarusian forces.
The whereabouts of the fighters has been a matter of considerable speculation since the Russian government-funded group, led by Yevgeny Prigozhin, staged a short-lived revolt against the leadership in Moscow last month.
Wagner troops have started work as instructors across a number of military disciplines at a camp in Osipovichi, about 100km south-east of the capital Minsk, the Belarusian Defence Ministry said.
The ministry released a video on its Telegram channel that purportedly showed men being trained on weapons at the camp.
A presenter in the video said the Wagner fighters were imparting their combat experience to the Belarusian armed forces.
Belarusian soldiers are also shown expressing gratitude for the lessons in the clip.
with AP
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