On Thursday, Yevgeny Prigozhin attacked his Russian partners in a gruesome, expletive-filled rant, filmed among dozens of Wagner troops' corpses.
The next day he said Wagner fighters would leave Bakhmut by 10 May.
But on Sunday Prigozhin said Moscow had agreed to provide the supplies "needed to continue fighting" in the city.
Prigozhin's apparent U-turn is not a huge surprise. He is a publicity seeker who has not followed through on previous threats.
Russian troops and fighters from Wagner, a private military company, have been trying to capture Bakhmut for months - despite its questionable strategic value.
Western officials believe thousands of Russian and Wagner troops have been killed in the fighting, and the eastern Ukrainian city has become a symbolic prize.
Yet - although Russian troops and Wagner fighters are on the same side - it is an uneasy alliance.
Prigozhin has regularly criticised Russian officials for what he claims is a lack of front-line support.
In his new statement, Prigozhin claimed that Gen Sergei Surovikin - who commanded Russia's forces in Ukraine between October and January - had been appointed to liaise between Russia's regular military and Wagner mercenaries.
"This is the only man with the star of an army general who knows how to fight," Prigozhin said. "No other army general is reasonable."
- Who is General Sergei Surovikin?
While Prigozhin didn't expressly reverse his pledge to withdraw troops from Bakhmut, he said his forces had been given permission to "act in Bakhmut as we see fit" - appearing to suggest they will remain.
The Kremlin has not commented on Prigozhin's latest statement.
Wagner has its own set of commanders, objectives and motivations, and Prigozhin is widely believed to hold his own domestic political ambitions.
Defence Minister Sergei Shoigu and Chief of the General Staff Valery Gerasimov have often been the focus for his anger, amid reports of infighting among different power groups in Vladimir Putin's entourage.
In his statement on Thursday, Prigozhin raged: "Shoigu! Gerasimov! Where is the... ammunition?... They came here as volunteers and die for you to fatten yourselves in your mahogany offices."
And he said Wagner's casualties were "growing in geometrical progression every day" because of the lack of ammunition.
At the time, Ukrainian officials expressed scepticism that Prigozhin truly intended to withdraw his forces from Bakhmut.
Deputy Defence Minister Hanna Maliar said on Friday that Wagner was actually redeploying mercenaries towards Bakhmut in a bid to capture the city before Tuesday's Victory Day celebrations in Russia.
In other developments in Ukraine and Russia:
- There was "mad panic" as Russia evacuated occupied towns near the Zaporizhzhia nuclear power plant
- A pro-war Russian writer is out of a coma, after his car was blown up by a car bomb
- Ukraine accused Russia of dropping white phosphorus bombs in Bakhmut
BBC