Which side had the upper hand was unclear, with "the situation changing from hour to hour," Oleksandr Stryuk, head of administration in Sievierodonetsk, said on television.
The city has become the main target of the Russian offensive in the Donbas - comprising Luhansk and Donetsk provinces - as the Kremlin's invasion grinds on in a war of attrition that has seen cities laid waste by artillery barrages.
"In the city, fierce street fighting continues...