"I will ask your dad not to punish you harshly", the president told the 30-year-old fighter from the mainly Muslim Dagestan region, adding that "you won worthily and convincingly".
UFC president Dana White says he should keep his belt, even if he is banned.
"In a family anything can happen, (but) we never allow ourselves to go beyond certain limits", Putin said. Tukhugov was pictured striking McGregor.
"Why no one says anything about insulting my homeland, religion, nation, family?"
Putin hailed Nurmagomedov's "convincing" victory in the highly anticipated mixed martial arts bout in Las Vegas on Saturday, and said the champion's decision to then climb over the cage and fight with members of McGregor's corner had been provoked by insults. He has also threatened to quit the organization if they decide to fire his compatriot and teammate Zubair Tukhugov.
"If you decide to fire (Tukhugov), you should know that you'll lose me too". But don't forget that it was Conor who had hit my another Brother FIRST, just check the video. if you decide to fire him, you should know that you'll lose me too. "I finished what [McGregor] had started".
McGregor's attack on the UFC bus stemmed from Nurmamedov and his team surrounding and intimidating Lobov earlier that weekend in April.
He then vowed to quit if his brother was sacked, and explained that he didn't care about whether or not he was paid: "If you decide to fire him, you should know that you'll lose me too".
McGregor tossed a steel dolly through a window on Nurmagomedov's bus in April in NY, a provocation the Russian noted in his message.
Nurmagomedov has one fight remaining on his contract. The UFC chose not to punish McGregor for his actions because of his crowd-pulling ability for the UFC.
Dana White will surely act on both the misconduct of Zubaira and the post by Khabib, but it seems both men will rise or fall together.