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Ukraine is planning seven humanitarian corridors for civilians to leave cities besieged by Russian forces, including the southern port of Mariupol.
Deputy Prime Minister Iryna Vereshchuk said people have already started leaving Sumy in the north-east under a local ceasefire.
At least 35,000 civilians evacuated besieged Ukrainian cities on Wednesday, President Volodymyr Zelenskyy said.
In a video address late on Wednesday, the Ukrainian leader said three humanitarian corridors had allowed residents to leave Sumy, Enerhodar and areas around Kyiv.
He said he hoped the evacuation would continue on Thursday with three more routes expected to open from Mariupol, Volnovakha in the south-east and Izium in eastern Ukraine.
Moscow and Kyiv agreed on Wednesday to open more corridors, offering a glimmer of hope for civilians trapped in bombarded regions.
A day earlier, more than 5,000 people were moved from Sumy, a city of 250,000 that lies close to the Russian border and the scene of heavy fighting.
But a number of attempted evacuations of Mariupol, which has been besieged by Russia for days, have failed, with Kyiv and Moscow blaming each other.
On Wednesday, a Russian strike destroyed a children's hospital in the city, triggering renewed global outrage two weeks into Moscow's invasion of its former Soviet neighbour.
Mariupol's mayor said more than 1,200 civilians have been killed in the siege, which has lasted more than a week.
The UN refugee agency UNHCR estimates the total number of people leaving Ukraine at 2.1 million to 2.2 million.