A local woman looks at an apartment building damaged by a Russian military strike in Vuhledar, Donetsk. Reuters

Since Moscow's invasion in late February, Western support has helped Ukraine hold off its neighbour's advances in many areas — including the capital Kyiv — but Russia is now focused on securing and expanding its gains in Donbas and the southern coast.

"The coming weeks of the war will be difficult, and we must be aware of that," Ukraine's President Volodymyr Zelensky said Monday in his nightly address after regional leaders and residents reported heavy bombardments.

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"The most difficult fighting situation today is in Donbas," Zelensky said, singling out the worst-hit towns of Bakhmut, Popasna and Severodonetsk.

The governor of Lugansk, in Donbas, said that Russia has sent thousands of troops to capture his entire region and that Severodonetsk was under massive attack, warning residents that it was too late to evacuate.

A residential building damaged by a Russian military strike in the town of Marinka, in Donetsk region. Reuters

"At this point I will not say: get out, evacuate. Now I will say: stay in a shelter," Sergiy Gaidai said on Telegram. "Because such a density of shelling will not allow us to calmly gather people and come for them."

Residents of Bakhmut, a crucial junction that serves as a command centre for much of the Ukrainian war effort, told AFP of the aerial onslaught they had suffered.

"I looked up from my prayers and heard a frightening sound," 82-year-old Maria Mayashlapak said next to the splintered remains of her home.

"Every day I pray to God asking to avoid injuries. God heard me. God is watching over me."

Ukrainian servicemen wave as they move toward the frontline in the eastern Ukranian region of Donbas. AFP

Zelensky said in his address that Russia has carried out nearly 1,500 missile strikes and over 3,000 airstrikes against Ukraine in the first three months of the war.

The president earlier warned elites gathered at the World Economic Forum in Davos -- from which Russians have been barred this year -- that slow-walking military aid was causing unnecessary deaths as Ukrainians are "paying dearly for freedom and independence".

He said that 87 people had been killed in a Russian attack earlier this month on a military base in the north, in what would be one of the largest single recorded strikes of the war.

Western countries have sent huge amounts of weapons and cash to Ukraine to help it repel Russia's assault, and punished Moscow with unprecedented economic sanctions.

But Zelensky said via videolink that tens of thousands of lives would have been saved if Kyiv had received "100 percent of our needs at once back in February", when Russia invaded.

He also ramped up his demands that Moscow be cut off from the global economy, calling for an international oil embargo on Russia, as well as punitive measures against all its banks and the shunning of its IT sector.

Agence France-Presse