Yevgeny Prigozhin has said that the Russian army will be in charge of the city by June 1, but Kyiv says it is still in charge of some parts of the city.
He said that his troops were ready to come back if the normal Russian army couldn’t handle the situation.
The war’s longest and bloodiest fight has been for the city.
On the Russian side, Wagner mercenaries have led the battle there, and Mr. Prigozhin said this week that 20,000 of its fighters had died in Bakhmut.
In a video sent out on Telegram from the destroyed city, Mr. Prigozhin said, “We are pulling units out of Bakhmut today.”
The video was taken in an area east of Bakhmut near a drugstore.
Mr. Prigozhin, who said on Saturday that the city had been taken, can be seen telling his men to leave ammo for the Russian army. He also says that some of the Wagner forces will stay behind to help the Russians.
“The military will stand up when things get tough,” he says, before telling two fights not to “bully the military.”
The boss of Wagner has gone after top Russian military officials more than once, criticizing them in public for not backing his troops. Last month, he even said he would pull his troops out of the city if they didn’t get the ammo they needed.
Even though Wagner says he is giving Bakhmut to Ukraine, Ukraine has not admitted that the city has fallen.
Hanna Maliar, who is the Deputy Minister of Defense for Ukraine, said on Thursday that the country’s troops still have control over part of the Litak district in the southwest of the city.
“The enemy has put regular army men in place of Wagner units in the suburbs. Wagner’s forces are still there inside the town,” she wrote on Telegram.
Analysts say that Bakhmut is not very important to Moscow from a strategic point of view, but that capturing it would be a symbolic win for Russia after the longest fight of the war in Ukraine so far.
Wagner’s mercenaries have been focusing on the city for months, and their expensive strategy of sending in waves of men over and over again seems to have slowly broken down Kyiv’s opposition.
Mr. Prigozhin, who is in charge of the private army of mercenaries, has become a key player in Russia’s full-scale attack of Ukraine, which started in February 2022.
He got thousands of criminals out of jail to join his group. It didn’t matter how bad their crimes were, as long as they agreed to fight for Wagner in Ukraine, they could join.
This week, Mr. Prigozhin said that about half of the 20,000 Wagner troops who died in Bakhmut were in prison.
The US said earlier this month that it thought more than 20,000 Russian soldiers had died and another 80,000 had been hurt in the fight for Bakhmut.
Ukraine has also lost a lot of people in Bakhmut, but the country hasn’t said how many.
If Russia took Bakhmut, it would be a little closer to its goal of controlling the whole Donetsk area. Donetsk was one of four parts of eastern and southern Ukraine that Russia took over last September after sham referendums.
But when Russia fought hard last summer to claim the town of Severodonetsk and Lysychansk, Ukraine quickly took back large chunks of land elsewhere.
Before the attack, there were about 70,000 people living in Bakhmut. Now, only a few thousand people live in the city, which was once known for its salt mines, gypsum mines, and huge winery.
