Kyiv reported "heated" fighting around its eastern city of Avdiivka on Saturday, saying Russian forces had "not stopped assaulting" the symbolic industrial hub for days in their attempt to surround it.
Ukraine last week said Russia had stepped up assaults on the frontline city, which lies just 15 km from Moscow-held Donetsk.
Avdiivka has been a symbol of Ukrainian resistance since 2014, after it briefly fell to Russian-backed separatists.
Russian forces now control territory to the east, north and south of Avdiivka.
"For the fifth day already, the enemy has not stopped either assaulting or shelling positions around the city," Vitaliy Barabash, the head of the city, said on Ukrainian television.
"It is very heated, very heated," he said of the fighting.
"They are trying to surround the city," Barabash added, claiming that Moscow was deploying "more new forces" to the area.
He described intense battles: "There is certainly no silence there at all. Shooting battles continue, both from the north and from the south of the city."
Kyiv's Interior Ministry said Russian shelling had "destroyed" a five-storey building in the city, saying it believed a man in his sixties was under the rubble but that it was "impossible to retrieve the body."
It urged residents still in Avdiivka to evacuate.
Some 1,600 civilians are believed to be in the city, which had a pre-war population of 31,000.
Ukrainian President Volodymyr Zelensky has said Kyiv was holding its ground in Avdiivka, but Moscow claimed it had improved its positions there.
Ukraine also said Saturday that a Russian attack killed an 11-year-old boy in the eastern village of Bagatyr, also in the Donetsk region, some 80 kilometres (50 miles) west of Avdiivka.
"The boy turned 11 just two days ago," Ukrainian police said in a statement.
It said his 31-year-old mother and younger brother were wounded and taken to hospital following the attack, which damaged around 20 homes, a church and a school.
Russia's intensified assault on Avdiivka has come after months of a Ukrainian counter-offensive, which has been slower than expected.
Russia meanwhile said it had "repelled enemy attacks" in several villages in eastern Ukraine, including in Andriivka -- an eastern village that Kyiv has claimed it recaptured but Russia says it controls.
