Serhiy Haidai said a hotel where the group met in Kadiivka, Luhansk, had been hit with major losses.
The BBC was unable to independently verify Wagner's presence at the hotel.
Fighting also raged in southern Ukraine over the weekend, with Russia targeting Odesa and Ukraine bombarding a target in the occupied city of Melitopol.
Wagner are state-sponsored mercenaries who act in the Kremlin's interests, according to Western experts.
The private military company, set up by Yevgeny Prigozhin, a former restaurateur and close associate of Russian President Vladimir Putin, has repeatedly been accused of war crimes and human rights abuses.
Wagner units have previously been deployed in Crimea, Syria, Libya, Mali and the Central African Republic.
In the Kadiivka strike, Mr Haidai said Russia had suffered "significant losses" and he expected "at least 50%" of the surviving forces to die due to a lack of medical treatment.
During a phone call with Ukrainian leader Volodymyr Zelensky, US President Joe Biden said Washington was prioritising efforts to help boost Ukraine's air defence systems.
The pair also spoke about Mr Zelensky's desire for a "just peace" with Russia "based on fundamental principles enshrined in the UN Charter", the White House said.
In Melitopol, pro-Moscow authorities said a Ukrainian missile attack had killed two people and injured 10. Images shared by a Moscow-installed official there showed a big fire.
"Air defence systems destroyed two missiles, four reached their targets," Yevgeny Balitsky, the Russia-installed governor of the city, said on the Telegram messaging app.
He added that a "recreation centre" where people were dining had been destroyed in the attack, and that Ukrainian forces had used US-supplied Himars rocket launchers.
This weapon has played a key role in Ukraine's counter-offensive, being used to target locations away from the frontlines, including Russia's command posts.
Ivan Fedorov, Melitopol's exiled mayor, said scores of "invaders" had been killed.
Melitopol has been under occupation since early March and is a major logistics hub for the Russian forces in the south-east.
The city, in the Zaporizhzhia region, is strategically located between Mariupol to the east, Kherson and the Dnipro River to the west, and Crimea to the south.
Ukraine says its efforts to retake occupied territory are continuing, despite the arrival of winter.
In recent weeks, most of the fighting has taken place in the east of the country, especially around the city of Bakhmut in the Donetsk region.
But on Saturday night, Oleksiy Arestovych, an adviser to President Zelensky, indicated that Melitopol could be a main target of Ukrainian forces.
"If Melitopol falls, the entire defence line all the way to Kherson collapses," he said in an interview.
If that happened, he added, "Ukrainian forces would gain a direct route to Crimea," the peninsula Russia annexed in 2014 and that the Ukrainians have vowed to retake.