The city of Sievierodonetsk in eastern Ukraine has not yet been blocked off by Russian troops, but they control about 80% of the area and have destroyed all three bridges leading out of it, an official said.
"There is still an opportunity for the evacuation of the wounded, communication with the Ukrainian military and local residents," Luhansk regional governor Serhiy Haidai told the Associated Press.
He acknowledged that Ukrainian forces have been pushed out to the industrial outskirts of the city because of "the scorched earth method and heavy artillery the Russians are using".
About 12,000 people remain in Sievierodonetsk, a city with a pre-war population of 100,000. More than 500 civilians are sheltering in the Azot chemical plant, which is being relentlessly pounded by the Russians, according to Mr Haidai.
A total of 70 civilians have been evacuated from the Luhansk region over the past 24 fours, the governor said.
Two people were killed and another wounded in the Luhansk region, according to Ukrainian authorities.
Ukrainian authorities said on Tuesday that they had received the bodies of 64 defenders of the Azovstal steel plant in Mariupol, in another body swap with Russia.
The statement by the Ministry for Reintegration of Occupied Territories said the exchange took place in the Zaporizhzhia region, but did not clarify how many bodies were returned to Russia.
It was one of several body swaps the warring sides have conducted. Earlier this month Moscow and Kyiv exchanged 160 bodies each.
Meanwhile, Ukraine said its air defence system shot down two Russian cruise missiles targeting the Odesa region.
Serhiy Bratchuk, spokesman for the Odesa regional military administration, thanked the country's air defence forces for striking down "two enemy" cruise missiles.
There was no independent confirmation and it was not clear if any missiles hit their targets.
Reports of overnight shelling came from other Ukrainian regions as well, with five people were wounded in the Kharkiv region.
Meanwhile, Pope Francis has blasted the "ferocity and cruelty" of Russian troops in Ukraine while praising the "heroism" and "courage" of Ukrainians in defending their land.
Francis made some of his most pointed comments about the war in a meeting with European editors of Jesuit journals last month, excerpts of which were published on Tuesday in Italian dailies La Stampa and Avvenire.
While sharply criticising Russia's invasion, Francis also insisted it was not a case of "good guys and bad guys" and that Moscow was in some ways provoked by Nato's expansion east.
"Someone might say at this point, 'But you are in favour of Putin!'. No, I'm not," Francis said.
"It would be simplistic and wrong to say such a thing. I am simply against reducing complexity to the distinction between good and bad, without thinking about roots and interests, which are very complex.
"While we see the ferocity, the cruelty of the Russian troops, we must not forget the problems to try to solve them."
In the interview, Francis confirmed he hopes to meet Russian Patriarch Kirill, who has justified the war, when the two are due to attend an interfaith meeting in Kazakhstan in mid-September.
A planned meeting in June was called off by both sides, Francis said, "so that our dialogue isn't misunderstood".
In Kazakhstan, he said: "I hope to be able to greet him and speak with him a bit as a pastor."
Francis went on at length to praise the courage of Ukrainians and reasserted their right to defend themselves while condemning what he said was the financial interest in the war by weapons manufacturers to "test and sell weapons".
"It's true the Russians thought it'd be over in a week. But they miscalculated," Francis said. "They found a courageous people, a people who are fighting to survive and have a history of fighting."
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