MOSCOW, July 13 (Reuters) - Russian President Vladimir Putin offered mercenary fighters with the Wagner group the opportunity to remain serving together in Russia after their revolt, he said in an interview published late on Thursday (Jul 13).

Putin, interviewed by the Russian daily Kommersant, said this was one of several offers he made at a meeting with around three dozen fighters and their founder Yevgeny Prigozhin late last month, five days after Wagner staged the abortive revolt against Russia's military hierarchy.

Under the offer, the fighters would stay under their current commander, who the newspaper identified only by his call sign of "Grey Hair".

Putin also said it was up to Russia's government and parliament to work out a legal framework for private military formations.

Kommersant said Putin spoke of meeting 35 Wagner fighters and Prigozhin in the Kremlin and offering them options for the future, including remaining under their commander of 16 months.

"All of them could have gathered in one place and continued their service," Kommersant quoted the president as saying. "And nothing would have changed. They would have been led by the same person who had been their real commander all that time."

As Putin is the army's commander-in-chief, he seemed to be implying that they would remain within the Russian military, although he did not say that explicitly.

"Many of then nodded when I said this," Kommersant quoted Putin as saying.

However, Prigozhin disagreed, it reported.

"Prigozhin ... said after listening: 'No, the boys won't agree with such a decision," Kommersant quoted Putin as saying.

Wagner fighters played a key role in the Russian army's advance into eastern Ukraine and were the driving force in the capture in May of the city of Bakhmut after months of battles.

But Prigozhin constantly accused the military of failing to back his men and Wagner fighters unhappy with the Defence Ministry's conduct of the war took control of the southern city of Rostov-on-Don on Jun 23 and began moving towards Moscow.

They halted their advance the next day after being offered a deal under which they could resettle in Belarus, along with Prigozhin. Any notion of pressing charges against Prigozhin was dropped.

Putin told the newspaper there was no possibility of Wagner remaining in its current form.

"Wagner does not exist," Putin told Kommersant. "There is no law on private military organisations. It just doesn't exist."