Ukrainian soldiers rest on the frontline near Kreminna, Luhansk region, Ukraine, Thursday, June 8, 2023. AP
Ukraine has not offered any confirmation but expectations have built for months over when its forces, bolstered with Western weapons and training, would launch a counter-offensive in a bid to reclaim land occupied by Russian forces.
The fighting comes as the humanitarian and environmental cost climbed after the destruction of the Kakhovka dam unleashed destructive flooding in a different part of Ukraine's south.
"At the moment, active combat is ongoing in the region between Orekhovo and Tokmak," Vladimir Rogov, an official with Russian occupation authorities, wrote on the Telegram messaging service, referring to a locality known in Ukrainian as Orikhiv.
Alexander Sladkov, a correspondent for Russian media, wrote on Telegram of "intense fighting" in the area.
"The enemy is undertaking incredible efforts, attacks. In vain. Our forces are holding on. The front line is stable," he wrote.
The information could not be independently verified.
Ukraine's army said only that "the adversary remains on the defensive" in Zaporizhzhia, in a Facebook post.
It said it destroyed four missiles and 10 drones, out of some 20 that Russia had fired at "military installations and critical infrastructure".
Russia said on Thursday that its forces had fought a two-hour battle with Ukrainian troops in the early hours in the Zaporizhzhia region, which neighbours the flood-hit areas.
Major impact of dam's destruction
Russian Defence Minister Sergei Shoigu said the Ukrainian offensive involved 1,500 soldiers and 150 armoured vehicles.
"The enemy was stopped and retreated after heavy losses," he said.
Ukrainian officials have said their forces are ready for a long-expected counteroffensive but that there would be no formal announcement when it begins.
Ukrainian Deputy Defence Minister Ganna Maliar said only that Russia was conducting "defensive actions" near the town of Orikhiv in the Zaporizhzhia region.
Parallel to the fresh fighting, the destruction of the major Russian-held dam on the Dnipro River on Tuesday left 600 square kilometres of the region under water.
Emergency services were racing to rescue people stranded by the flood-swollen waters of the Dnipro, which have forced thousands to flee.
Ukrainian authorities said water levels in a reservoir which had been created by the Kakhovka dam had fallen "below the critical point of 12.7 metres (42 feet)".
They said the reservoir was no longer able to supply households and the cooling ponds at the Zaporizhzhia nuclear power station, Europe's largest.
However late Thursday the International Atomic Energy Agency (IAEA) said he nuclear plant was continuing to receive water from the reservoir after the dam was damaged.
The plant's six reactors have been shut down but they still need cooling water to ensure there is no nuclear disaster.
Ukraine meanwhile called on Europe to double power supplies to two gigawatts.
Ukraine accuses Russia, whose forces control the dam area, of blowing up the dam, while Russia accuses Ukraine hitting it with artillery.
Ukrhydroenergo, the dam's operator, said it was most likely mined from the inside.
The emergency service has warned the flood water has dislodged land mines that pose a threat to civilians.
The government has also sounded the alarm over the environmental impact, calling it "a crime of ecocide".