(NewsNation Now) — With the number of Ukrainian refugees leaving their country nearing 700,000, the United Nations says Russia’s invasion of Ukraine could become Europe’s largest refugee crisis of the century.

Hundreds of thousands of people have been going by car, train and even on foot to avoid the fallout from the Russian offensive that started last week and has killed 136 civilians as of Tuesday. They’ve been heading to neighboring countries to the West: Romania, Slovakia, Hungary and Moldova. So far, Poland has taken in more than half of the refugees.

“We have reinforced our operations to respond as quickly and effectively as possible,” The United Nation’s Refugee agency, UNHCR, said in a Tuesday Twitter post, where it announced that 660,000 refugees have now fled Ukraine.

Holding her dog in her arms at Kyiv’s Central Train Station, Kyiv resident Tatyana Dichenko said she does not want to leave her home— but she doesn’t have a choice.

“This is a big tragedy for me to leave my city,” she said. “I don’t know if I’m going to come back or not, and I don’t want to leave but it’s completely dangerous to stay here.”

Many in Ukraine have had to shelter themselves from bullets, missiles or shells, going underground to subway stations, basements and other places for protection.

One woman fleeing Ukraine said she was doing so “to save my life, the life of my baby and my husband’s life.”

Hundreds of Ukrainians found refuge inside one Polish school.

“Russia, stop Putin. We don’t want to fight with anyone, we want to be in our home with our parents, children,” one woman at the school said. “We don’t want to go (to) any countries.”

Support for displaced Ukrainians is flooding in from all corners of the world. Airbnb is offering to host the refugees for free.

Brian Chesky, the rental company’s CEO, said he had a conversation with Airbnb’s executive team over the weekend that spurred the offer.

“I asked them a hypothetical question, ‘Imagine it was World War II and Airbnb was around, how would we want to have helped? What would we have wanted to do?'” he said. “When you do an exercise like that, you realize that you would regret not doing more if you could have and didn’t.”

“What we think we can do is provide housing for up to 100,000 refugees,” Chesky added.

Stays for refugees will be funded by Airbnb, donors to the  Airbnb.org Refugee Fund and Airbnb hosts.

Those interested in opening their homes to support the effort can learn more at airbnb.org/help-ukraine.

The United Nations and its partners launched a coordinated emergency appeal for $1.7 billion to deliver the humanitarian support it says 12 million people need.

“Families with small children are hunkered down in basements and subway stations or running for their lives to the terrifying sound of explosions and wailing sirens,” UN humanitarian chief Martin Griffiths said in a statement. “Casualty numbers are rising fast. This is the darkest hour for the people of Ukraine. We need to ramp up our response now to protect the lives and dignity of ordinary Ukrainians. We must respond with compassion and solidarity.”

While it’s estimated that 4 million people will leave Ukraine, 12 million are expected to stay. Some have even returned— about 80,000, according to the State Border Guard Service of Ukraine. Most of them were men who worked or temporarily lived outside of Ukraine, who came back to “protect its sovereignty and territorial integrity,” the border guard service said.

The Associated Press and Reuters contributed to this report.