Russia's invasion of Ukraine has left hundreds of thousands of people without electricity or water, and the UN fears up to 5 million people could be forced to flee the country.
Some 368,000 people have fled abroad from the fighting in Ukraine, the UN refugee agency said on Sunday, citing data provided by national authorities.
Over the weekend as fighting intensified and Russian forces pressed towards Kyiv, home to nearly 3 million, it was estimated the number of internally displaced people rose to more than 160,000.
Several thousand refugees have already crossed into neighbouring countries including Moldova, Romania and Poland, UN refugee agency spokesperson Shabia Mantoo said.
"We are looking at ranges of 1-3 million into Poland for example ... A scenario of 1 to 5 million including all surrounding countries," Afshan Khan, UNICEF’s regional director for Europe and Central Asia, told a UN briefing in Geneva.
The UN said Polish border authorities had reported about 100,000 people arriving in recent days.
"While the scale and scope of displacement will only likely become apparent in the coming days and weeks, Ukrainian authorities estimate that as many as 5 million people could flee the country, triggering a refugee crisis that will test response capacities in neighbouring countries," the OCHA said.
Some Ukrainians walked many kilometres through the night to escape the conflict while others fled by train, car or bus, forming long lines at border crossings.
Video posted to social media showed a packed train station full of people reportedly trying to make it to Poland.
Across central Europe, authorities set up makeshift reception centres in tents where people could get medical aid and process asylum papers, while thousands of volunteers drove up to the borders with donations of collected food, blankets and clothes, offering transport services.
German railway operator Deutsche Bahn said on Sunday it would offer free trips from Poland to Germany for refugees from Ukraine.
In Hungary, the immigration authority said only 10 people had applied for asylum so far, as an overwhelming majority of people who came over were ethnic Hungarians or already had the right to stay in the country. Thirty-five people have applied for asylum in Slovakia.
Romanian authorities said about half of those who had entered the country so far, or about 20,000 people, had already left to elsewhere in Europe.
The Czech government said a train with military aid for Ukraine had arrived in Poland, loaded with machine guns, sniper rifles, pistols and artillery ammunition.
Romania will send fuel, ammunition, bullet-proof vests, helmets, military equipment, food and water worth 3 million euros ($4.6 million) to Ukraine and has offered to care for the wounded in military and civilian hospitals, government spokesman Dan Carbunaru said on Sunday.
Some Ukrainian men were heading back into Ukraine from Poland to take up arms against the Russian forces, while Ukrainian Foreign Minister Dmytro Kuleba called for foreign fighters to join Ukrainian forces as part of the International Legion of Territorial Defense of Ukraine.
After Ukraine enacted martial law and restricted border passage for men between 18 and 60 years old, it was mostly women and children crossing.
Long queues at border crossings
Iryna, 36, set out from Kyiv on Thursday with her mother and two girls, aged two and four, before crossing into Ubla in Slovakia.
"We left my husband there, so he is still there supporting our government," she said on Friday at a hotel in the border town of Snina.
"We pray for Ukraine and I hope everything will be fine."
On the border with northern Romania, women were crying as they said goodbye to male loved ones before setting off to cross into Sighetu Marmatiei, a Reuters witness said.
Long queues formed as cars waited to board a ferry over the Danube River into Isaccea, a town between Moldova and the Black Sea, local media in Romania showed.
One family from Chernivtsi in western Ukraine waited 20 hours before being able to cross the border into Siret in northern Romania.
Natalia Murinik, 14, cried as she described saying goodbye to grandparents who could not leave Ukraine.
"It really hurt, I want to go home," she said.
The border post in Siret was crowded with Ukrainians on Saturday. Humanitarian groups set up tents a few miles in and offered food and drink to those arriving.
Despite the welcome, teenager Natalia Murinik's family did not know where they were going next.
"We don't have a clue. We're waiting for our friends and then we'll think," she said.
Slovak authorities urged people to donate blood and set up hospitals with 5,380 beds assigned for the army or NATO use.
Across central Europe, on NATO's eastern flank, volunteers were putting up messages on social media to organise housing and transport for people arriving from the borders.
People waiting all day for basics
Oliver Hochedez, head of aid group Malteser International's emergency relief department, said it was becoming harder to find essential supplies in Ukraine.
"What is especially needed are everyday medicines, as well as cots, blankets, food and cash to provide for the many people affected," he said.
"At the moment, there is no way to get through. The streets in the big cities are full of people who want to get themselves and their families to safety.
"In some places there is only rationed food and a maximum of 20 litres of gasoline per car.
"The queues at the stores are huge. People wait outside pharmacies all day."
Due to the "already dire humanitarian situation in the Donbas region" before the invasion "around 2.9 million people already required humanitarian assistance", the OCHA said.
"[It is] a figure that is expected to rise exponentially as a result of the intensification of armed conflict," it said.
According to the OCHA, there has been "significant infrastructural damage" that has cut power and water.
Some communities cannot reach food and other basic supplies because roads and bridges have been damaged by shelling, it said.
Ukraine's ambassador to the US, Oksana Markarova, said authorities had been gathering evidence of shelling of residential areas, kindergartens and hospitals to submit to The Hague as possible crimes against humanity.
The UN Office for the Coordination of Humanitarian Affairs said on Saturday there had been at least 240 civilian casualties, including at least 64 dead.
The death toll included three children, with 33 more among those injured, according to Save the Children.
ABC/wires
