Conflict raged northwest of Kyiv on Saturday and other cities were encircled, with Ukrainian officials saying heavy shelling and threats of Russian air attacks were endangering attempted evacuations.
Deputy Prime Minister Iryna Vereshchuk had said the government planned to use agreed humanitarian corridors out of the besieged southern port city of Mariupol as well as towns and villages in the regions of Kyiv, Sumy and some other areas.
But the governor of the Kyiv region said fighting and threats of Russian air attacks were continuing during evacuation attempts and the Donetsk region's governor said constant shelling was complicating bringing aid into Mariupol.
Air raid sirens blared across most Ukrainian cities on Saturday morning urging people to seek shelters, local media reported.
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The bombardment has trapped thousands of people in besieged cities and sent 2.5 million Ukrainians fleeing to neighbouring countries.
The exhausted-looking governor of Chernihiv, around 150 km northeast of Kyiv, gave a video update in front of the ruins of its Ukraine Hotel, which he said had been hit on Saturday.
"There is no such hotel anymore," Viacheslav Chaus said, wiping tears from his eyes. "But Ukraine itself still exists, and it will prevail."
Russian rocket attacks destroyed a Ukrainian airbase and hit an ammunition depot near the town of Vasylkiv in the Kyiv region on Saturday morning, Interfax Ukraine quoted Vasylkiv Mayor Natalia Balasynovych as saying.
Moscow has denied targeting civilians what it calls a special operation to demilitarise Ukraine and unseat leaders it refers to as neo-Nazis. It has not responded to Ukrainian challenges to provide evidence.
Ukraine said it expected a new wave of attacks on the regions around the capital Kyiv, the country's second city Kharkiv and Donbass in the east, where Russian-backed separatists have expanded their control.
Britain's defence ministry said on Friday that Russian forces could launch an offensive on the capital Kyiv in a few days. In an update on Saturday, it said fighting northwest of the capital continued, with the bulk of Russian ground forces 25 km (16 miles) from the centre.
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The cities of Kharkiv, Chernihiv, Sumy and Mariupol remained encircled under heavy Russian shelling, it said.
Efforts to isolate Russia economically have stepped up, with the United States imposing new sanctions on senior Kremlin officials and Russian oligarchs on Friday.
European Commission President Ursula von der Leyen said the EU would on Saturday suspend Moscow's privileged trade and economic treatment, crack down on its use of crypto-assets, and ban the import of iron and steel goods from Russia, as well as the export of luxury goods in the other direction.
Moscow said on Saturday the European Union would end up paying at least three times more for oil, gas and electricity.
"I believe the European Union would not benefit from this – we have more durable supplies and stronger nerves," Russian foreign ministry official Nikolai Kobrinets told Interfax.
#BayraktarTB2 attacking what appears to be a Russian command post near Kyiv. https://t.co/pxz42Lvjhy
— Oryx (@oryxspioenkop) March 11, 2022
As the Russian invasion entered its third week, its forces kept up their bombardment of cities across the country on Friday. Satellite images showed them firing artillery as they advanced on Kyiv.
As hundreds sheltered in metro stations in Kharkiv, Nastya, a young girl lying on a makeshift bed on the floor of a train carriage, said she had been there for over a week, unable to move around much and ill with a virus.
"I'm scared for my home, for the homes of my friends, very scared for the whole country, and scared for myself of course," she said.