Mission accomplished. After having claimed responsibility for the capture of the city of Bakhmut in eastern Ukraine last weekend, the Wagner mercenary group began on Thursday to transfer their positions to the troops of the Russian Defense Ministry, with which their leader, Yevgeny Prigozhin maintains a tense, dog-faced rivalry that lasts for months.

“Today we are starting to withdraw the Bakhmut units. By June 1, most of them will be reinstalled in rear bases. We are handing over our positions to the military,” the oligarch who maintains close ties to the Kremlin said in a video broadcast by his press service on Telegram.

From Kyiv Hanna Maliar, Ukraine’s deputy defense minister, confirmed for her part that Wagner’s paramilitaries had left their positions “on the periphery of Bakhmut” to transfer them to regular Russian troops. “Wagner’s units remain in the city of Bakhmut. Our soldiers control the Litak neighborhood in the southwestern suburbs,” she remarked.

Prigozhin claimed last Saturday to have completely taken this stronghold in eastern Ukraine for which Russia has been fighting for eight months. From Moscow’s point of view, it is an important enclave, because it can allow its troops to continue advancing to the west, attack the cities of Slaviansk and Kromatorsk to try to gain full control of the Donetsk province, which together with that of Luhansk form the Donbass.

On Sunday the Russian Ministry of Defense confirmed the statement of the controversial businessman and the head of the Kremlin, Vladimir Putin, congratulated both.

But Ukraine has denied that the town, which before the conflict had a population of 70,000, has fallen into Russian hands. Kyiv claims that in recent days it has recovered 20 square kilometers north and south of the city.

The end of Wagner’s operations in Bakhmut, which Moscow calls Artiomovsk, the name the city had until 2016, also comes days after an incursion by dozens of saboteurs in the Russian region of Belgorod, bordering Ukraine.

The attack, claimed by groups of Russian volunteers who declare themselves anti-Kremlin and are fighting side by side with Ukrainian forces, exposed Russia’s defenses of its own borders. One of them, Russia’s Freedom Legion, said on Wednesday that it had only two fatalities and 10 wounded.

The Russian Army needed more than 24 hours, using aviation and artillery, to expel them from their territory and push them back to Ukraine. According to defense spokesman Lieutenant General Igor Konashenkov, Moscow eliminated “more than 70 terrorists.”

In his video, Prigozhin avoided the harsh criticism that has usually accompanied his public messages. After greeting his men and wishing them a safe return, he announced that the Wagners would continue to serve in Moscow. “We retire, we will rest, we prepare, then we will receive new tasks,” she added.

In an interview conducted before the withdrawal of his paramilitaries began, Prigozhin acknowledged that some 10,000 Russian convicts recruited by his group died in the Battle of Bakhmut. In an interview with a pro-government political scientist, Konstantin Dolgov, he admitted to having enlisted some 50,000 men in Russian prisons.

Prigozhin claimed to have lost a total of 15,000-16,000 men in this battle, the bloodiest of the current conflict.