Wagner head Yevgeny Prigozhin on Tuesday announced his forces had control over Soledar but said battles were still raging in the city center. On Wednesday, he made no mention of continuing clashes.
"I want to confirm the complete liberation and cleansing of the territory of Soledar from units of the Ukrainian army ... Ukrainian units that did not want to surrender were destroyed," he said in a statement.
Wagner forces "killed about 500 people. The whole city is littered with the corpses of Ukrainian soldiers."
Minutes before, Ukrainian President Volodymyr Zelenskyy had mocked earlier Russian claims to control part of the town and said fighting continued.
Moscow has deployed Wagner Mercenaries to eastern Ukraine in increasing numbers recently. Observers say Russia is using them as front-line forces to absorb attacks and casualties that otherwise would be imposed on Moscow's own troops.