The mass exodus of Ukrainian refugees showed no signs of abating on Monday, with the United Nations (UN) estimating that more than 500,000 people have already fled Ukraine due to the Russian invasion.

Long lines of cars and buses have been blocked at border checkpoints in Poland, Hungary, Slovakia, Romania and Moldova, which is not a member of the European Union (EU). Others cross the borders on foot, dragging their wheeled suitcases away from the war.

Several hundred refugees have gathered at a temporary reception center in the Hungarian border village of Beregsurany, awaiting transport to movement centers where they can be taken to Hungary or other countries.

As Lusa reports, 24-year-old Maria Pavlushko, a technology and information project manager in Zhytomyr, a town about 100 kilometers west of Kiev, said she was on vacation in the snow in the Carpathian mountains when she got the news that the Russian invasion had begun.

"My grandmother called me to tell me there was war in the city," he said.

Pavlushko plans to travel from Hungary to Poland, where his mother lives. But his grandmother is still in Zhytomy, he said, and his parents stayed behind to join the fight against the invading forces sent by Vladimir Putin.

"I am proud of him. Many of my friends, many young people will...kill [the Russian soldiers]," she noted.

Many of the refugees in the reception center in Beregsurany, as in other border areas of Western 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 the west of the country, came with 18 other Indian students to the Hungarian border. The young man said they hoped to reach Hungary's capital, Budapest, where the Indian government arranged a repatriation flight.

Although the war has not yet reached Ternopil, Masroor Ahmed said that "there may be shelling in the next hour, next month or next year.

"We're not sure, that's why we left that city," he pointed out.

Hungary, in a reversal to its opposition to immigration and rejection to accepting refugees in the Middle East, Africa and Asia, has opened the borders for all people who are leaving Ukraine, including third country nationals who can prove Ukrainian residency.

As part of an agreement with some foreign governments, Hungary has set up a "humanitarian corridor" to escort non-Ukrainian citizens from the border to airports in the cities of Debrecen and Budapest.

Priscillia Vawa Zira, a Nigerian medical student in the eastern Ukrainian city of Kharkiv, said she fled to Hungary when the Russian military started the military offensive.

"The situation was very terrible. You had to run, because explosions were popping up here and there every minute, run to the bunker," he mentioned.

The high commissioner of the UN Refugee Agency (UNHCR), Filippo Grandi, wrote on Twitter this Monday that more than half a million refugees have already fled Ukraine to neighboring countries.

In the face of the war spreading across the Ukrainian territory, non-governmental organizations (NGOs) are calling for "unconditional humanitarian access" to bring aid to civilians, the injured or refugees.

"All combatants [...] must accept that there is a humanitarian space and unconditional humanitarian access so that the most vulnerable can be rescued," said French International Committee of the Red Cross (ICRC) spokesman Frédéric Joli.