According to UN, another 13 million people are believed to be trapped in the war-affected areas of Ukraine.
The number of people fleeing Ukraine to escape Russia's invasion has passed 5 million in Europe's worst refugee crisis since the end of World War Two, UN refugee agency said on Wednesday.
Russia's invasion has triggered a massive displacement of people in the nearly eight weeks since it began, including more than 7 million Ukrainians within the country. UN data showed that 5.03 million had fled Ukraine as of Wednesday.
A child holds a dog as evacuees wait before boarding a bus to leave the Mariupol city. Reuters
"They have left behind their homes and families," UNHCR head Filippo Grandi said on Twitter. "Many would do anything, and some even risk going back, to see their loved ones." "But every new attack shatters their hopes. Only an end to the war can pave the way for rebuilding their lives."
Russia launched what it calls a "special military operation" on Feb.24 saying its aim was to demilitarise and "denazify" its southern neighbour.
Kyiv and its Western allies reject that as a false pretext for an unprovoked land grab.
Local residents push a cart with a child past buildings destroyed during conflict in Mariupol. Reuters
Most refugees have crossed to the European Union (EU) through border points in Poland, Slovakia, Hungary and Romania where volunteers and governments have scrambled to help those arriving, mostly women and children, find jobs, accommodation and to provide them support.
The refugee numbers were unprecedented for central Europe, said Jakub Andrle, the migration programme coordinator at People in Need, a Prague-based aid group operating in Ukraine.
"It is also important to remember the numbers can increase rapidly from day-to-day depending on the situation on the ground."
A woman holding her child cries as she arrives at the Siret border crossing between Romania and Ukraine. AFP
More than half the refugees have entered the EU through Poland where many had family and other connections living in the region's largest pre-war Ukrainian community.
In central and eastern Europe, many residents rushed to the border at the outset of the war, bringing supplies to weary refugees, many of whom endured long and harrowing journeys to safety.
Now the focus has shifted to the longer term support as cities reach housing capacity and many refugees remain in temporary housing with families or hotels that need the space for the upcoming tourist season.
"The first response was really good but now governments need to think about the long-term perspective," said , People in Need migration programme coordinator Katarina Pleskot Kollarova.
"It is getting difficult, for example, to find places in Prague and it is harder to keep big families together."
President Zelensky said conditions in Mariupol, which has seen the worst fighting of the nearly eight-week long war, continued to worsen, though Reuters witnesses said a few dozen civilians managed to leave the city on Wednesday in a small bus convoy.
Jill Biden called the show of solidarity "amazing" but also "just the beginning.” She said it was inspiring for Romanians "to welcome all these refugees into their homes and offer them food and clothing and shelter and give them their hearts.
On average, every day over the last 20 days in Ukraine, more than 70,000 children have become refugees," James Elder, spokesman for the UN children's agency UNICEF, told reporters in Geneva.
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