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A senior Russian military commander has been killed in a battle on the edge of the eastern Ukrainian city of Kharkiv, Ukraine's defence ministry says.
Maj-Gen Vitaly Gerasimov, chief of staff and deputy commander of the 41st Army, died along with other Russian officers, the report says.
Russia has not commented.
Ukraine has begun evacuating civilians from the town of Irpin near Kyiv and more evacuations are expected from the northern town of Sumy.
It comes after Russian and Ukrainian officials agreed to establish humanitarian corridors.
"As of 09:30 [07:30 GMT], more than 150 people have been evacuated and activities are under way [from Irpin]," said Kyiv Region Governor Oleksiy Kuleba, quoted by Reuters.
The head of Poltava Region, the destination of evacuees from Sumy, also said several dozen buses had been sent to the city to pick up evacuees.
International students are expected to be among the evacuees.
The corridors are expected to stay open until 21:00, but so far there has been no confirmation of evacuations from other cities.
Ukrainian cities have continued to come under heavy bombardment from Russian forces and many civilians have so far been prevented from fleeing after previous attempts to evacuate them failed.
Ukraine had described Russia's evacuation plans, many of which involve fleeing residents being sent to Russia, as cynical.
In Sumy, authorities say children were among 10 people killed in artillery strikes late on Monday.
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The Ukrainian defence ministry statement said Maj-Gen Gerasimov was a veteran of the second Chechen war in 1999-2000, the Russian military campaign in Syria and the annexation of Crimea in 2014.
It is based on a purported intercept of expletive-ridden phone conversations between Russian security officials which has not been verified.
In the first conversation, the officials complain that secure communication lines have been lost and describe the situation as "very tight".
In the second, another official mentions that Maj-Gen Gerasimov was killed and gives several other names of wounded.
The audio was originally posted with the Ukrainian defence ministry statement but has since been taken down, though it has been posted on YouTube.
The news came as UK Defence Secretary Ben Wallace offered a gloomy assessment of Russia's prospects, saying the war could end with the Russian army "turning in on itself".
He told the BBC that Russian President Vladimir Putin was a "spent force in the world" and that even if Russia won the war in Ukraine it would face "decades of occupation which I don't think [Mr Putin] will be able to sustain".