"The human cost of this battle is very high for us. It is simply terrifying," Zelenskyy said on Telegram in his daily address to the Ukrainian people.

"The battle for the Donbas will without doubt be remembered in military history as one of the most violent battles in Europe," he added.

Ukrainian Defence Minister Oleksiy Reznikov last week said up to 100 of his troops were dying daily and 500 sustaining injuries in the intense fighting against Russian troops, in a rare public disclosure of casualty figures.

Zelenskyy on June 1 said his army was losing "between 60 and 100 soldiers" every day.

Russian troops have advanced on Severodonetsk as part of their large-scale offensive in the eastern Donbas region after failing to take the capital Kyiv.

Severodonetsk is the largest city in the eastern Lugansk region, which forms part of Donbas, still under Ukrainian control.

"We are dealing with absolute evil. And we have no choice but to move forward and free our territory," Zelenskyy added in his Telegram address, calling on the West supply more weapons to the Ukrainian army.

Lugansk regional governor Sergiy Gaiday on Monday said Russian forces control 70 to 80 percent of Severodonetsk but had not encircled or captured it amid fierce Ukrainian resistance.

He added that evacuations from the city and access to it were impossible as the last bridges had been blown up.

Severodonetsk's twin city of Lysychansk was also coming under intense Russian shelling, Gaiday said.

Lugansk and neighbouring Donetsk make up the mainly Russian-speaking Donbas region, where Ukrainian forces have fought pro-Moscow separatists since 2014.