Ukrainian President Volodymyr Zelenskyy is describing the situation in Sieverodonetsk as "severe," with fighting taking place in "every metre" of the embattled city.
Mr Zelenskyy says Russia is using its conscripted troops as 'canon-fodder', claiming Russia's army has lost 40,000 soldiers in June alone.
Russian forces have taken most of the city but Ukrainian troops remain in control of an industrial area and the Azot chemical plant where hundreds of civilians are still sheltering.
Local officials say Russian forces blew up a bridge linking Sievierodonetsk with Lysychansk across the river, cutting off a possible evacuation route for civilians.
People could be seen leaving buildings, clutching clusters of bags and getting into police vehicles to escape the intense Russian shelling.
One woman said she was leaving because the shelling killed a girl in front of her building.