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The number of people who have crossed the country's borders stood at 7,252,542 since the Russian invasion began on February 24, the UNHCR’s tally showed on Wednesday.
There were 4,793,216 refugees from Ukraine recorded across Europe, with Poland, Russia and Moldova the top host countries, it said.
The war in Ukraine has sent refugees fleeing from all parts of the country as fighting exploded in the capital, Kyiv — where Ukrainian fighters forced Russia’s military to withdraw — and in the east where Russia wants control of the Donbas region.
Ukrainian refugees arrive in Europe - in pictures
Few will be returning to the industrial city of Severodonetsk in the near future after Ukrainian forces pulled back from the city following a fierce Russian assault, the regional governor said on Wednesday.
Russia has concentrated its troops and firepower on the small eastern city in the Donbas as it tries to secure the surrounding province.
Ukraine has vowed to fight there for as long as possible, saying the battle could help shape the war's course.
“ … Our [forces] now again control only the outskirts of the city. But the fighting is still going on, our [forces] are defending Severodonetsk, it is impossible to say the Russians completely control the city,” governor Serhiy Gaidai said.
He said earlier that Russian forces would step up their bombardment of both Severodonetsk and its smaller twin city of Lysychansk on the west bank of the Siverskyi Donets River.
Ukrainian police released footage showing the evacuation of elderly people from Lysychansk. Removals had been stopped for about a week by shelling of the main road.
Russian forces have 10 times more equipment than Ukrainian troops in some areas of Severodonetsk, said Ukraine's defence ministry spokesman Oleksandr Motuzyanyk.
Two provinces, Luhansk and Donetsk, form the Donbas, which is claimed by Russia for its separatist proxies who have held eastern parts of the region since 2014.
Russian forces have been attacking the Ukrainian-held part of the Donbas from the north, east and south in an effort to encircle Ukrainian forces in the area.
In Sloviansk, one of the main Donbas cities still held by Ukraine, women with small children lined up to collect aid while other residents carried buckets of water across the city.
Most residents have fled but authorities say about 24,000 remain in the city, in the path of an expected assault by Russian forces regrouping to the north.
Ukrainian President Volodymyr Zelenskyy's office said two people were killed and two others wounded in the Luhansk region in the 24-hour period, while five civilians were wounded in Donetsk, and four were killed and 11 wounded in the Kharkiv region.
In Kharkiv, Ukraine's second-largest city, residents cleaned up rubble from shelling carried out the previous day.
Ukraine pushed Russian forces back last month from the city's outskirts, but Russia still strikes it sporadically.