Russia says its forces entered the northeastern border town of Vovchansk, near Ukraine’s second-largest city, Kharkiv.
Ukraine says there is still heavy fighting going on there.
Russia intensified its attacks on the region following Friday’s surprise cross-border incursions, seizing at least nine villages and settlements in one of the most significant ground attacks since the full-scale invasion of Ukraine in February 2022.
Thousands of civilians have fled to Kharkiv and there are concerns among Ukrainian commanders about what could happen if Russian forces came within artillery range of the city.
The Ukrainian army said Russia had mobilized “significant forces” – up to five battalions – in its latest offensive, acknowledging that it had been “tactically successful”.
But in a statement, the army said Russia had lost more than 100 soldiers in one day, adding that it was taking measures to repel the advancing forces.
Vovchansk, located 74 kilometers from Kharkiv, has been heavily bombed in recent days and authorities in the surrounding region say Moscow is now attacking towns with glide bombs.
Although an important city in the region, Vovchansk has no specific military importance, although its capture would be a blow to Ukrainian morale.
Kharkiv regional chief Oleh Syniehubov said Russia was deliberately trying to widen the front line, attacking in small groups in new directions.
He told local television that Ukrainian forces were holding back Russian troops, but warned that fighting could spread to new settlements, according to Reuters.
Nearly 6,000 people were evacuated in the region, he said, adding that 30 settlements were hit by mortars or artillery.
While it is thought that this cross-border Russian incursion is still unlikely to be able to take Kharkiv, its gradual approach to this new front line in the northeast only increases the anxiety of those living there.
Frustrated Ukrainian troops told the BBC that Russian soldiers were initially able to simply “walk in” to the region due to the lack of defenses.
Kostyantyn Tymchenko, who lives in Vovchansk, was among those who left the city for the relative safety of Kharkiv and said he was shocked by how fierce the fighting was.
“Half a kilometer away there is already fighting, automatic weapons,” he said.
“On the one hand [of the Vovcha River] they are [Russians]on the other – ours.
“The tanks are constantly approaching, firing back and then leaving. I thought there would be no problem. I was shocked. I wish I had known in advance.”
Away from Kharkiv, two people were killed in shelling in the Russian-controlled city of Donetsk in eastern Ukraine, the Russian-installed mayor said.
And at least three people were killed in an attack on an industrial zone in Krasnodon, known as Sorokyne in Ukrainian, a part of eastern Ukraine controlled by Russia, the Moscow-inaugurated local governor said.
Ukraine has not commented on these incidents.
Russia also said it had shot down 31 Ukrainian drones in several regions of annexed Crimea.
It comes after Russian officials said at least 15 people were killed when a section of an apartment block collapsed in the Russian border town of Belgorod when it was hit by fragments from a Ukrainian missile that had been shot down.
A Ukrainian security source said Ukrainian forces attacked an oil terminal and an electrical substation in western Russia.
