Russian armored vehicles in an undisclosed area. Photo courtesy of Russian Defense Ministry via The Russian News Agency TASS
Russian-installed official in the region Vladimir Rogov said offensive actions were concentrated around two towns: Orikhiv, around 50 kilometres (30 miles) south of Ukrainian-controlled regional capital Zaporizhzhia, and Hulyaipole, further east.
"The front is mobile, especially in two directions: Orikhiv and Hulyaipole," Rogov was quoted as saying by the Ria Novosti news agency.
He said there was active fighting in those areas, according to the agency.
"The initiative is in our hands."
The Russian army later claimed for a second day in a row that it had taken "more advantageous lines and positions" after "offensive operations" in Zaporizhzhia.
It claimed to have hit Ukrainian positions in the village of Lezhyno, outside the regional capital of Zaporizhzhia, which has not fallen to Ukrainian forces.
AFP was not able to verify this information.
In its daily report on Sunday, the Ukrainian army said "more than 15 settlements were affected by artillery fire" in Zaporizhzhia.
Earlier this week, Rogov announced a "local offensive" around Orikhiv and said the Russian army had taken control of the village of Lobkove, near the Dnipro river.
He also said this week that fighting has "sharply increased" in the southern region.
The front in southern Ukraine has been considerably quieter recently than in the east, with Moscow withdrawing from the major city of Kherson in November.
Russia claims to have annexed the Zaporizhzhia region along with three other Ukrainian regions, but does not control it in its entirety.
While Moscow controls large swathes of the southern part of the region, its main city Zaporizhzhia and northern part did not fall to Russian forces.
Russia has vowed to push Ukrainian forces out of them.