Ukrainian presidential adviser Mykhailo Podolyak said the Wagner mercenary group had "almost nullified" Russian President Vladimir Putin. Wagner fighters are said to have left Rostov-on-Don.
Wagner units are continuing their withdrawal and forces are departing "without incident" from the the southern Russian region of Voronezh, according to the area's governor.
Ukraine has not claimed responsibility for explosions Monday at two airbases hundreds of miles inside Russian territory, one of which houses nuclear-capable bombers.
A blast and fire suspended traffic on a key bridge linking Russia to the occupied Crimean Peninsula early on October 8, sparking speculation that Ukrainian forces were again targeting operational support for Moscow's seven-month-old full-scale invasion.