BEREGSURANY, Hungary (AP) — The mass exodus of refugees from Ukraine to the eastern edge of the European Union showed no signs of stopping Monday as they flee Russia's burgeoning war, with the U.N. estimating that more than 500,000 people have already escaped.

Long lines of cars and buses were backed up at checkpoints at the borders of Poland, Hungary, Slovakia, Romania and non-EU member Moldova. Others crossed the borders on foot, dragging their possessions away from the war and into the security of the EU.

Several hundred refugees were gathered at a temporary reception center in the Hungarian border village of Beregsurany, where they awaited transportation to transit hubs that could take them further into Hungary and beyond.

Maria Pavlushko, 24, an information technology project manager from Zhytomyr, a city around 100 kilometers (60 miles) west of the Ukrainian capital Kyiv, said she had been on a skiing holiday in the Carpathian mountains when she got word from home last week that Russia's invasion had begun.

"I'm waking up just because my granny called me saying there is war in the city," she said.

Pavlushko plans to travel on from Hungary to Poland, where her mother lives. But her grandmother is still at home in Zhytomyr, she said, and her father has stayed behind to join the fight against the invading Russian forces.

"I am proud about him," she said. "A lot of my friends, a lot of young boys are going ... to kill (the Russian soldiers)."

Many of the refugees at the reception center in Beregsurany, as in other border areas in Eastern Europe, are from India, Nigeria and other African countries, and were working or studying in Ukraine when the war broke out.

Masroor Ahmed, a 22-year-old Indian medical student studying in Ternopil in western Ukraine, came with 18 other Indian students to the Hungarian border. He said they hoped to reach the capital of Budapest, where India's government has organized an evacuation flight for its citizens.

While Ternopil has not yet experienced violence in the war, he said, "it is supposed to. It might be that there is bombing next hour, next month or next year. We are not sure, that's why we left that city."

Hungary has opened its borders to all refugees fleeing Ukraine, including third-country nationals that can prove Ukrainian residency. The government has set up a "humanitarian corridor" to escort non-Ukrainian nationals from the border to airports in the city of Debrecen and the capital, Budapest.

The welcome that Hungary is now showing Ukrainians is very different from the unwelcoming stance they have had toward refugees and migrants from the Middle East and Africa in recent years. Hungary built a wall to keep them out when 1 million people, many Syrians fleeing war, arrived in Europe in 2015.

U.N. High Commissioner for Refugees Filippo Grandi tweeted on Monday that more than 500,000 refugees have now fled from Ukraine into neighboring countries.

Shabia Mantoo, a UNHCR spokeswoman, said the latest and still growing count had 281,000 in Poland, more than 84,500 in Hungary, about 36,400 in Moldova, over 32,500 in Romania and about 30,000 in Slovakia.

The rest were scattered in unidentified other countries, she said.

In Poland, the country that has reported the most arrivals, trains continued to bring refugees into the border town of Przemysl on Monday. In winter coats to protect them against near-freezing temperatures, many carried small suitcases as they lined up at the platform to exit the station.

Natalia Pivniuk, a young Ukrainian woman from the western city of Lviv, described people crowding and pushing to get on the train as it prepared to depart for Poland, which she said was "very scary and dangerous physically and dangerous mentally."

"People are under the stress, people are distorted and when people are scared they become egoist and forget about everything," she said. "People are traumatized because they were on that train."

Otoman Adel Abid, a student from Iraq, also fled from Lviv after he said panic broke out among many in the city.

"Everyone ran to buy some food and we heard some bombs everywhere," he told The Associated Press. "After that we directly packed our bag and clothes and some documents and we run to the train station."

In the Romanian town of Siret on Monday, EU commissioner for home affairs Ylva Johansson visited a border crossing where thousands of refugees are entering from neighboring Ukraine as they flee the conflict with Russia.

Johansson, who visited some of the humanitarian stations at the border, commended the "heartwarming" cooperation between volunteers and the authorities, and said that the EU is united "in a way we have never seen before."

"I am here today because I wanted to visit and see with my own eyes, to talk directly to local authorities, local citizens, migrants about the situation and the challenges," Johansson told the media at the border.

She said it was a "very difficult time where we see war in Europe again, where we see aggression, invasion from (Russian President Vladimir) Putin towards a sovereign, neighboring country."

Johansson, who will meet later on Monday with Romanian President Klaus Iohannis and Prime Minister Nicolae Ciuca, said that Europe is "showing that we are based on other values than Putin."

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Monika Scislowska in Warsaw, Poland, Stephen McGrath in Siret, Romania, and Jamey Keaten in Geneva, contributed to this report.