“Elon Musk, a word of advice: Don’t measure strength against that of Putin’s,” wrote Mr Kadyrov.
“Vladimir Vladimirovich (Mr Putin’s middle name) will look unsportsmanlike when he beats the hell out of you, a much weaker opponent.”
“Therefore you’ll need to pump up those muscles in order to change from the gentle (effeminate) Elona into the brutal Elon you need to be. I propose training at one of several centres in the Chechen Republic,” he added.
He then offered Mr Musk training in three Chechan institutes: The Russian Special Forces University, the Akhmat Fight Club and the Grozny Chechen State Television and Radio Broadcasting Company.
“You will return from the Chechen Republic a completely different person Elona, that is, Elon,” he said.
In response, Mr Musk said in a tweet: “Thank you for the offer, but such excellent training would give me too much of an advantage.”
“If he is afraid to fight, I will agree to use only my left hand and I am not even left-handed,” he added and signed off the message as “Elona”.
The Twitter reply to the Chechen leader came after Mr Musk challenged the Russian president to a “single combat” fight over his invasion of Ukraine.
He tagged the official Kremlin Twitter account in one of the posts, asking in Russian whether it would “agree to this fight”. He is yet to receive any official response from the Russian government.
Mr Musk has condemned Russia’s invasion of Ukraine, both on his Twitter feed and through his companies.
He has also mocked Russian officials on social media, as well as providing Starlink space internet equipment to Ukraine.
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