Smoke rises after an airstrike in Lviv, Ukraine. File/Reuters

Ukrainian President Volodymyr Zelensky said his country's forces were "doing everything" to stop the Russian offensive, with fierce battles in the east and the south.

Kyiv said on Friday it had launched new air strikes in the captured southern region of Kherson, one of the first areas to be taken by Russia after the February 24 invasion.

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But Zelensky said Friday "very difficult battles" were ongoing, including in the eastern Donbas region where Moscow has concentrated its firepower, especially around the eastern industrial city of Severodonetsk.

Ukrainian President Volodymyr Zelensky speaks in Kyiv. File photo

"Ukrainian troops are doing everything to stop the offensive of the occupiers," Zelensky said in an address.

"As much as the heavy weapons, modern artillery — all that we have asked and continue to ask our partners for — allow them to."

In the Mykolaiv region near the front line in the south, the regional governor stressed the urgent need for international military assistance.

"Russia's army is more powerful, they have a lot of artillery and ammo. For now, this is a war of artillery... and we are out of ammo," Vitaliy Kim said.

Ukrainian forces are "doing everything" to stop the Russian offensive.

"The help of Europe and America is very, very important because we just need ammo to defend our country."

Zelensky said in his address that Ukraine must "not allow the world to divert its attention away from what is happening on the battlefield".

In the town of Lysychansk, located just across a river from Severodonetsk, people told AFP about their stark choice: stay and brave the shelling, or flee and abandon their homes.

Yevhen Zhyryada, 39, said the only way to access water was by heading to a water distribution site in the town.

"We have to go there under shelling, and under fire," he said.

"This is how we survive."

Agence France-Presse