President Volodymyr Zelenskiy says his forces will not yield "a single centimetre" in battles for control of eastern Donetsk region while Russian-installed officials have described Ukrainian forces moving into one 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, the theatre of the heaviest fighting in the country since Russian forces invaded their neighbour in late February.
"The activity of the occupiers remains at an extremely high level - dozens of attacks every day," Zelenskiy said in his nightly video address.
"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 claimed to have annexed in late September.
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 on Tuesday that residents had seen tanks and that fierce fighting was going on.
"They got into (radio) 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 told RIA.
Kirill Stremousov, deputy head of the Russian-installed administration in Kherson region, said Ukrainian forces had tried to advance on three fronts, including Snihurivka.
Vitaly Kim, the Ukrainian governor of Mykolaiv region, strongly suggested that Ukrainian forces had already evicted Russian forces from the area. He quoted what appeared to be a conversation between Russian servicemen. "The Russian troops are complaining that they have already been thrown out of there," a statement on Kim's Telegram channel said.
There was no official word on the situation in the town from military officials in either Ukraine or Russia.
On Tuesday night, a Ukrainian military statement accused Russian troops of continuing to loot and destroy infrastructure in Kherson, where a showdown has been looming for weeks in the only regional capital Russia has captured intact since its invasion.
"On 7th November, a convoy of trucks passed over the dam of the Kakhova hydroelectric station loaded with home appliances and building materials," the statement said.
Russian forces were dismantling mobile phone towers and taking away equipment, it said.
Zelenskiy also said in his address that around 4 million people were without power in 14 regions plus the capital Kyiv, but on a stabilisation rather than an emergency basis.
Russian missile and drone attacks have targeted Ukraine's energy infrastructure in the past few weeks as winter approaches when mean temperatures typically drop to several degrees below zero Celsius.
The UN General Assembly is due to vote next week on a draft resolution recognising that Russia must be responsible for reparation in Ukraine for the injury, including any damage, caused by "internationally wrongful acts."
Three-quarters of the 193-member General Assembly voted in March to denounce Russia's invasion and then again in October to condemn Moscow's attempted annexation of parts of Ukraine.