Ukraine President Volodymyr Zelensky speaks to the media in Kyiv. File photo

The cities of Severodonetsk and Lysychansk have been targeted for weeks as the last areas in the eastern Donbas region of Lugansk still under Ukrainian control.

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President Volodymyr Zelensky said Monday the human cost of the battle for the region was "simply terrifying".

Zelensky expressed confidence in Ukraine's ability to reclaim territory, calling on the nation's allies to send more weapons.

"We just need enough weapons to ensure all of this. Our partners have them."

Captured Ukrainian ammunition are seen in a labyrinth of the Metallurgical Combine Azovstal. AP

Presidential advisor Mikhaylo Podolyak on Monday listed items he said the Ukrainian army requires, including hundreds of howitzers, tanks and armoured vehicles.

"Being straightforward -- to end the war we need heavy weapons," he tweeted.

Severodonetsk under siege

Regional governor Sergiy Gaiday said Monday that Ukraine's forces had been pushed back from Severodonetsk's centre after a weeks-long Russian offensive.

"They destroyed all the bridges, and getting into the city is no longer possible. Evacuation is also not possible," he told Radio Free Europe.

He said Russian forces control 70 to 80 per cent of the city but had not captured or encircled it.

A man rides a bicycle in front of a building destroyed by attacks in Borodyanka, Ukraine, on Sunday. AP

Last week, Ukraine's defence minister said up to 100 of his troops were dying daily and 500 sustaining injuries. Previously, Zelensky had estimated 60-100 Ukrainian soldiers were dying daily.

With the screws tightening on the Lugansk region, Ukrainian forces have two choices: "to surrender or die", said Eduard Basurin, a representative for pro-Russian separatists.

The capture of Severodonetsk would open the road to Sloviansk and another major city, Kramatorsk, in Moscow's push to conquer Donbas, a mainly Russian-speaking region partly held by pro-Kremlin separatists since 2014.

Agence France-Presse