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, 41st Army chief of staff, died along with other Russian officers, the report says.

Russia has not commented, but if confirmed he would be their second officer of this rank to be killed.

Ukraine has begun evacuating civilians from the town of Irpin near Kyiv and the northern city 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.

Sumy Region Governor Dmytro Zhyvytsky, quoted by Reuters, said buses with evacuees had departed from the city for Poltava, further south.

International students were 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.

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.

A former assistant defence minister of Ukraine, Andriy Ryzhenko, told the BBC World Service's Newsday programme it was not normal practice for high-ranking Russian officers to be in command posts, and his death showed how intensive the warfare was.

The reported death comes a week after the death of Andrey Sukhovetsky, another deputy commander of the same army, was confirmed by Russian media.

Ukraine says it has killed more than 11,000 Russian troops. Russia has confirmed some 500 dead.

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 BBC Radio 4's Today programme 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".