Russia said on Friday it was sending reinforcements to the Kharkiv region in eastern Ukraine, where Kyiv says it has re-taken dozens of settlements as part of a broader counter-offensive.
President Volodymyr Zelensky said in his evening address that Ukrainian troops had retaken 30 areas from Russian forces.
"We are gradually taking control over new settlements. We are returning the Ukrainian flag and protection for our citizens everywhere," he said, calling on Ukrainians to report any crimes committed by the occupying forces.
In the Kharkiv region, Ukrainian officials have exhumed two bodies in a village recently recaptured from Russia, part of an investigation into a possible war crime.
Grakove village was the scene of fierce fighting in the early weeks of Russia's invasion.
Russian state media broadcast footage of military vehicles travelling along paved roads and dirt tracks in Kharkiv region, emblazoned with the letter "Z", the symbol of Moscow's invasion.
A Moscow-installed official, Vitaliy Ganchev, said in televised remarks that "fierce battles" were under way near the town of Balakliya, which Ukraine said it had recaptured on Thursday.
"We do not control Balakliya. Attempts are being made to dislodge the Ukrainian forces, but there are fierce battles, and our troops are being held back on the approaches," Ganchev said.
"Now Russian reserves have been brought there, our troops are fighting back," he added.
- Fresh shelling of nuclear plant -
The head of the International Atomic Energy Agency (IAEA) meanwhile warned of "dramatic" developments at the Russian-controlled Zaporizhzhia nuclear power plant in southern Ukraine where recent fighting had "compromised the safe operation" of the facility.
IAEA Secretary General Rafael Grossi warned that fresh shelling near the plant had caused a blackout in the nearby town of Energodar.
That jeopardised the safe running of the plant, he said.
"This is completely unacceptable. It cannot stand," he said, insisting on "the immediate cessation of all shelling in the entire area".
Petro Kotin, the head of Ukraine's nuclear energy agency, told AFP that Russian forces had tortured staff at the nuclear power station, and that at least two people had been killed.
"Two people were beaten to death. We do not know where about ten people are now, they were taken (by the Russians) and after that we have no information about their whereabouts," he said.
In the recently recaptured village of Grakove, where Ukrainian officials exhumed two bodies Friday, resident Sergiy Lutsay spoke to journalists about what he had seen.
Russian soldiers had forced him to bury the bodies at gunpoint soon after the war began, he said.
"They came to my house, I was with my father, aged 70," he told journalists. "I was scared that they would threaten him."
"They told me to come to dig a hole."
He would not confirm a police statement that said that at least one of the two men killed had had his ears cut off.
- 'Huge costs' for Russia: Blinken -
US Secretary of State Antony Blinken said Russia's push to reinforce Kharkiv showed Moscow was paying "huge costs" in its bid to capture and then hold Ukrainian territory.
"There are a huge number of Russian forces that are in Ukraine and unfortunately, tragically, horrifically President (Vladimir) Putin has demonstrated that he will throw a lot of people into this at huge cost to Russia," he said.
He was speaking during a visit to Brussels on Friday for talks with NATO Secretary General Jens Stoltenberg.
A day earlier he paid a surprise visit to Kyiv during which he unveiled another $2.8 billion in military aid and hailed Ukraine's "clear and real" frontline gains.
Late on Thursday, Zelensky shared footage showing camouflage-clad Ukrainian soldiers holding his country's blue-and-yellow flag over Balakliya.
The town, which had been under Russian control for around six months and had a pre-war population of around 30,000 people, fell early on to Russian forces who invaded in February.
Now, Russian officials in the Kharkiv region say they are evacuating civilians towards Russia "until the situation stabilises".
On the Ukrainian side however, Kharkiv regional governor Oleg Synegubov warned people not to return to newly recaptured areas while "cleaning and demining" took place.
In the area around Kharkiv city, Ukrainian forces penetrated 50 kilometres (30 miles) beyond Russian lines and took back more than 20 towns and villages, military officials said.