Ukraine's President Volodymyr Zelenskyy said his forces would not yield "a single centimetre" in battles for the eastern Ukrainian region of Donetsk, while Russian-installed officials said Ukrainian forces were moving into a southern town with tanks.
The focal points of the conflict in the industrial region of Donetsk are around the towns of Bakhmut, Soledar and Avdiivka, which have seen the heaviest fighting since Russian forces invaded Ukraine in late February.
"The activity of the occupiers remains at an extremely high level - dozens of attacks every day," Zelenskyy said in his nightly video address late on Tuesday.
"They are suffering extraordinarily high losses. But the order remains the same - to advance on the administrative boundary of Donetsk region. We will not yield a single centimetre of our land," he said.
The region is one of four Russia said it annexed in September. Fighting had been going on there between the Ukrainian military and Russian proxy forces since 2014, the same year Russia annexed Crimea in the south.
A Russian-installed mayor in the town of Snihurivka, east of the southern city of Mykolaiv, was cited by Russia's RIA news agency as saying residents had seen tanks and that fierce fighting was going on.
"They got into contact during the day and said there were tanks moving around and, according to their information, heavy fighting on the edge of the town," the mayor, Yuri Barabashov, said, referring to the residents.
"People saw this equipment moving through the streets in the town centre," he said.
Kirill Stremousov, deputy head of the Russian-installed administration in the Kherson region, said on the Telegram messaging service that Ukrainian forces had tried to advance on three fronts, including Snihurivka.
Vitaly Kim, the Ukrainian governor of the Mykolaiv region, apparently quoting an intercepted conversation between Russian servicemen, suggested that Ukrainian forces had already pushed the Russians out of the area.
"Russian troops are complaining that they have already been thrown out of there," Kim said in a statement on his Telegram channel.
There was no official word on the situation in the town from military officials in either Ukraine or Russia.
Ukrainian forces have been on the offensive in recent months while Russia is regrouping to defend areas of Ukraine it still occupies, having called up hundreds of thousands of reservists over the past month.
Kyiv-based military analyst Oleh Zhdanov said on Tuesday that 21 Russian conscripts had surrendered to Ukrainian forces around Svatove in Luhansk region.
"These poor mobilised men - really poor, they had had nothing to eat or drink in three days - of course, they decided to surrender," Zhdanov said on his YouTube channel.