Russia's Defense Ministry said on Friday that the "Akhmat" group of Chechen special forces were waging an offensive near the town of Mariinka, in the eastern Ukrainian region of Donetsk.
Together with the Wagner mercenary group led by Yevgeny Prigozhin, troops from Russia's Chechen Republic have been one of the main driving forces behind Moscow's offensive in Ukraine.
Akhmat commander Apti Alaudinov said on Thursday that his forces were being moved to "another area" in preparation for a counter-offensive, but did not say where the troops were or where they were going.
Unlike Prigozhin, who has repeatedly lambasted Russia's military leadership, Chechen leader Ramzan Kadyrov has recently refrained from echoing criticism of the defense ministry.
Members of the two groups have since openly sparred, with one of Kadyrov's close allies on Thursday casting Prigozhin as a blogger who yells all the time about problems.