WARSAW, Poland — Tens of thousands of Ukrainians rushed to the borders as invading Russian troops pressed their advance into Ukraine and toward the country’s capital Saturday in Europe’s largest ground war since World War II.

Some walked many miles through the night while others fled by train, car or bus, forming lines miles long at border crossings. They were greeted by waiting relatives and friends or headed on their own to reception centers organized by governments.

With the world revolted at Russia’s unprovoked attack on Ukraine, a Western-looking democracy, there was a huge outpouring of support for the fleeing Ukrainians. This included an unconditional welcome from nations like Poland that often did not want to accept those fleeing conflict and poverty in the Middle East and Africa in past years.

Nearly 120,000 people have so far fled Ukraine into Poland and other neighboring countries in the wake of Russian invasion, the U.N. refugee agency said Saturday. The number was going up fast as Ukrainians grabbed their belongings and rushed to escape from a deadly Russian onslaught on their nation, including an attempt to take the capital of Kyiv.

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 couldn’t leave the country.

“It really hurt, I want to go home,” she said.

The largest numbers were arriving in Poland, where 2 million Ukrainians have already settled to work in recent years, driven away by Russia’s first incursion into Ukraine when it annexed Crimea in 2014 and seeking opportunities in the booming economy of the European Union neighbor.

Poland’s government said Saturday that more than 100,000 Ukrainians had crossed the Polish-Ukrainian border in the past 48 hours alone. At the Medyka border crossing, the line of vehicles waiting to enter Poland stretched 15 kilometers (9 miles) into Ukraine.

Poland declared its border open to fleeing Ukrainians, even for those without official documents, and dropped its requirement to show a negative COVID-19 test.

“We will help everyone,” the Polish Border Agency said. “We will not leave anyone without help.”

On Saturday, Poland sent a hospital train to pick up those wounded in the war in Mostyska, in western Ukraine, and bring them to the Polish capital of Warsaw for treatment. The hospital train left the border town of Przemysl and has five carriages to transport the wounded and four others stocked with humanitarian aid for Ukraine’s Lviv district.

Those arriving were mostly women, children and the elderly after Ukrainian President Volodymyr Zelenskyy on Thursday banned men of military age from 18 to 60 from leaving the country. Some Ukrainian men were reportedly heading back into Ukraine from Poland to take up arms against the Russian forces.

“Almost 116,000 have crossed international borders as of right now. This may go up, it’s changing every minute,” said Shabia Mantoo, the spokeswoman of the U.N. High Commissioner for Refugees, on Saturday morning. “It’s very fluid and changing by the hour.”

Mantoo said most Ukrainians were heading to neighboring Poland, Moldova, Hungary, Romania and Slovakia but some even fled into Belarus — from which some Russian forces entered Ukraine. Some planned to head further on to other countries in Europe.

The agency expects up to 4 million Ukrainians could flee if the situation deteriorates further.

The border post in Siret was crowded with Ukrainians arriving on Saturday. A few miles in, humanitarian groups had set up tents and offered food and drink to those arriving.

But the fate of teenager Natalia Murinik’s family was now uncertain, and they didn’t 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.