The UN has reported that at least 100,000 people have been displaced by the war, and predicted the number could rise as high as 4 million. The first Ukrainian refugees have started to arrive in Romania, Hungary and Poland. Some of them spent the night at a train station in neighboring Poland, where reception centers were being hastily set up.
More people were trying to flee from Kyiv to western Ukraine "with whatever they are able to carry," DW correspondent Fanny Facsar said from Ukraine.
What is it like fleeing the war in Ukraine?
Dima Khilchenko, a consultant for DW Academy, shared his experience of moving his family out of Kyiv to the west of the country.
"It was quite complicated yesterday," Khilchenko said. "We woke up at 5:30 a.m. because we heard the explosion and it's very hard to confuse this sound with something else and we understood straight away that the war has started."
Khilchenko said moving his two children from Kyiv to his hometown in western Ukraine took about 10 hours, a journey he said usually takes three.
"It was massive traffic jams, and you could see buildings on the horizon burning, and smoke was going out of them. It was pretty scary."
Thursday was mainly about making sure the family is safe, Khilchenko said. "To my understanding, Kyiv will be the main goal [of the invasion], and we already hear the news," he said, so he moved his family to the west for now but will potentially have to send them abroad as the situation escalates.
"My daughter, who is 6-years-old, asked me if I'm going to war, and I said if I have to, I will, and of course, she asked me not to do that. But you see, like when your country is invaded, who, if not us, will do it," he said, adding that he has no military training and has never shot a gun.
'All you have in your head is fear': DW's Dima Khilchenko fled Kyiv with his family
A humanitarian crisis?
As fighting intensifies, a lot of people are leaving from the east to the west of Ukraine, Ole Solvang of the Norwegian Refugee Council told DW.
Solvang stressed that the humanitarian situation had already been dire in Ukraine before the full-scale war.
"It is very important to keep in mind here that even before the latest hostilities, there were very significant humanitarian needs in the country," Solvang said.
About 3 million people were estimated to be in need of humanitarian assistance, and the number will likely increase amid the Russian offensive, he added.
The UN announced it was allocating $20 million (€17.9 million) to increase humanitarian operations in Ukraine.
UN Secretary-General Antonio Guterres said the UN and its partners "are committed to staying and delivering, to support people in Ukraine in their time of need... regardless of who or where they are."
Ukrainian refugees 'will be a political challenge for Europe': DW's Richard Walker
What is Europe doing to help?
On Thursday, European Commission President Ursula von der Leyen said the EU was "immediately" ready to host and welcome refugees fleeing Ukraine. Von der Leyen also vowed financial assistance to Ukraine.
The EU's interior ministers are due to meet this weekend for talks over Ukraine, including the expected arrival of a large number of refugees to EU countries, which have so far expressed solidarity with those fleeing.
German Interior Minister Nancy Faeser said Germany would offer support to Poland and other countries in eastern Europe that are receiving large numbers of Ukrainian refugees.
Hungary's Foreign Minister Peter Szijjarto said his country was opening a humanitarian corridor for citizens from third-party countries, like Iran or India, who are fleeing Ukraine. Those citizens would be allowed in Hungary without visas and then taken to the nearest airport in the northeastern Debrecen city, Szijjarto said.