Convoys of civilians are due to leave several towns near the Ukrainian capital, Kyiv, according to regional leader, Oleksiy Kuleba.
Ukraine says it has agreed a 12-hour ceasefire with Russia for six routes in the war zone, and Mr Kuleba said the first groups had already left.
Russian shelling has continued with further reports of civilian deaths.
Russian forces surrounding the southern port city of Mariupol have destroyed a maternity hospital, Ukraine says.
Olena Stokoz of Ukraine’s Red Cross said “the whole city remains without electricity, water, food, whatever and people are dying because of dehydration.
“We will continue trying to organise that (vacuation) corridor,” she told the BBC.
A local Ukrainian official, Pavlo Kirilenko, posted a video on Facebook which he said showed the ruined hospital – gutted, smoking buildings and debris.
Earlier, Ukrainian Foreign Minister, Dmytro Kuleba, said”almost 3,000 newborn babies lack medicine and food” in Mariupol, and “Russia continues holding hostage over 400,000 people” there.
Ten people died in Severodonetsk in the east and five people were killed in Malyn near Kyiv, Ukraine says.
Sumy governor, Dmytro Zhyvytskyi, said a night air raid on Monday flattened six houses and three children were among 22 people killed. “Three bombs in one evening… It was a terrible night,” he said.
Fighting is continuing north and north-west of Kyiv as Russian forces continue their offensive.
Ukrainian Member of Parliament (MP), Inna Sovsun, told the BBC that the Russian military was struggling to make significant progress. Air raid sirens were heard again in cities across Ukraine on Wednesday.
Ukraine’s armed forces agreed to stop firing on Wednesday along six evacuation routes for 12 hours, from 09:00 to 21:00 local time (07:00 to 19:00 GMT). They urged Russian forces to fulfil their commitment to the local ceasefires.
Mr Kuleba, who heads Kyiv’s regional administration, said civilians were due to leave towns such as Bucha and Hostomel to the north-west of Kyiv, several of them under Russian occupation. “I really hope everything will be fine and we’ll look after our people.”
Police said convoys of buses and other vehicles were on their way and they asked residents to follow their instructions.