Ukrainian refugees cross in Moldova at Palanca village | Ciro Fusco

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Ukraine will on Wednesday try to evacuate civilians through six "humanitarian corridors", including from the besieged southern port city of Mariupol, Deputy Prime Minister Iryna Vereshchuk said.

She said in a video statement that Ukrainian armed forces had agreed to stop firing in those areas from 9 a.m. until 9 p.m. (0700-1900 GMT)and urged Russian forces to fulfil their commitment to local ceasefires.

She said the corridors that would open would go from Mariupol to Zaporizhzhia; Enerhodar to Zaporizhzhia; Sumy to Poltava; Izyum to Lozova; Volnovakha to Pokrovsk; and from severaltowns around Kyiv which she identified as Vorzel, Borodyanka, Bucha, Irpin and Hostomel to the capital.

"I appeal to the Russian Federation: You have undertaken official public commitments to cease fire from 9 a.m. to 9 p.m. We have had negative experiences when the commitments that were undertaken did not work," Vereshchuk said.

She was referring to several failed attempts to open safe corridors for trapped civilians in the past few days. Each side blamed the other for their failure.

About 5,000 people did however manage to flee the northeastern city of Sumy through a humanitarian corridor on Tuesday, the regional governor said.

Civilians in private cars started leaving Sumy on Wednesday after a "humanitarian corridor" was established for a second successive day, Sumy Mayor Oleksandr Lysenko said in televised comments.

The number of people fleeing Ukraine since the Russian invasion began has probably now reached 2.1-2.2 million people, the head of the United Nation's refugee agency UNHCR said on Wednesday.

United Nations High Commissioner for Refugees Filippo Grandi told a news conference during a visit to Stockholm that "the time is now to try to help at the border", rather than discussions on the division of refugees between countries.

Grandi added that non-EU-member Moldova in particular was very vulnerable in the current situation.