Russia is concentrating its forces and firepower on the last Ukrainian stronghold in the eastern region of Luhansk.
While the battle for Severodonetsk hits maximum intensity, Ukrainian forces are pushing to recapture the southern region of Kherson.
Russia's defense ministry confirmed on Monday its troops were attacking Ukrainian positions in both Donetsk and neighboring Luhansk.
The region's governor says Ukrainian troops have been pushed back to a chemical plant. Speaking to the Associated Press, he said much of Severodonetsk is on fire and Russian shelling has been relentless.
Ukraine's Deputy Prime Minister has expressed concerns about the hundreds of civilians sheltering in Severodonetsk. Iryna Vereshchuk has also urged residents in the southern region of Kherson to flee, even if it means going to Russian-controlled Crimea.
She said, "The liberation of the areas under Russian control is coming soon. If we keep getting weapons from Europe and the US, our military has a fighting chance. Kherson is ours.
She also pointed out the Russian military could use residents as human shields to prevent a counterattack by the Ukrainian military.
Kherson's governor echoed that warning, adding it's impossible for civilians to escape into Ukrainian territory.
Hennadiy Lahuta said, "The situation here is serious. Since the start of the invasion, Russia has chosen not to set up a humanitarian corridor."
He also said there is a serious shortage of medicine and other supplies.