Authorities in Mariupol were seeking to evacuate some residents on Sunday under a new ceasefire plan for the encircled Ukrainian city, as the United Nations said Europe faced its fastest growing refugee crisis since World War Two.

With Russia's assault on Ukraine in its 11th day, the Mariupol city council said its evacuation plan would run from noon (1000 GMT) to 9 p.m. (1900 GMT), after a ceasefire plan he previous day earlier collapsed with each side blaming the other.

It was not immediately possible to verify if the evacuation had begun from the coastal city, which has faced heavy bombardment for days, trapping residents without heat, power and water.

Kyiv has renewed its call for the West to toughen sanctions beyond existing efforts that have hammered Russia's economy, and has requested more weapons, including a plea for Russian-made planes, to help it repel Russian forces.

Moscow and Kyiv traded blame over the collapse of Saturday's ceasefire to allow civilians to flee Mariupol and another southern city, Volnovakha.

"They’re destroying us," Mariupol mayor Vadym Boychenko told Reuters in a video call, describing the plight of the city of 400,000. "They will not even give us an opportunity to count the wounded and the killed because the shelling does not stop." 

Russia has repeatedly denied targetting civilian areas.

Elsewhere in Ukraine, police reported Russian shelling and air raids in the northeast Kharkiv region.

Moscow said it had struck and disabled Starokostiantyniv air base in west Ukraine using high-precision weapons.

Ukrainian President Volodymyr Zelenskiy said Russia was preparing to bombard another southern city, Odessa.

"Rockets against Odessa? This will be a war crime," he said in a televised address.

The World Health Organization said there had been several attacks on Ukrainian healthcare facilities during the conflict. The attacks caused multiple deaths and injuries, WHO chief Tedros Adhanom Ghebreyesus said in a Twitter message, but gave no details.