Thousands more refugees crossed into Eastern Europe on Thursday, March 17, many hoping that ongoing peace talks between Moscow and Kyiv may end the war soon, though more people were expected to flee in the days ahead.

As the war in Ukraine entered its fourth week, about 3.2 million have fled abroad, United Nations data showed on Thursday in what has become Europe’s fastest growing refugee crisis since World War Two.

While the numbers arriving in the frontline states – Poland, Slovakia, Hungary, Romania and Moldova – have slowed in recent days, Hungarian Prime Minister Viktor Orban said he expected a “bigger wave” next week.

“The war is not subsiding, but spreading; and as it spreads, there is the risk that next week will see the arrival of more people in Hungary, presenting us with a huge challenge,” he said in a video posted on his Facebook page late on Wednesday.

“They are not only fleeing from areas threatened by war, but also from war zones themselves.”

One of them was Alla Klochko from Mirnohrod in Donetsk, the region in eastern Ukraine that separatists have declared an independent republic but is contested by Kyiv and is at the center of fierce fighting between Ukraine and Russia.

The 31-year-old was hoping she could stay near Warsaw, find work and enrol her eight-year-old daughter Alisa, who loves playing the piano, in a Polish school.

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“I hope that, if our delegation reaches an agreement and at the end there will be peace, I hope that Ukraine will not lose our part of the territory, our Donetsk, because Donetsk region is Ukrainian,” she said.

“We are a part of Ukraine, have always been and hope that this will stay like that,” she said from Przemysl train station, a transit hub near the Ukrainian border. “We speak Russian, but we are Ukrainians.”

Moving west

The majority of European countries have offered to take in refugees in the past few weeks to alleviate the pressure on Ukraine’s neighbors. German police have recorded 187,428 refugees – mostly women and children – as of Thursday, the interior ministry said while Spain has registered about 4,500 so far.

Amid the unrelenting fighting, both Ukraine and Russia have spoken of progress in their bilateral talks.

Ukrainian officials have said they think Russia is running out of troops to keep fighting and could soon come to terms with its failure to topple the Ukrainian government. Moscow has said it is close to agreeing a formula that would keep Ukraine neutral, long one of its demands.

“I hope that this will end soon. Everybody says that it has to … I don’t know,” said Ekaterina Herman, 27, who arrived in Poland late on Wednesday with her two-year-old.

“I am planning to come back to Ukraine.”

Meanwhile, refugees across the region were trying to establish some kind of normalcy.

At a supermarket-turned-shelter in Rzeszow, south-eastern Poland, volunteers and children played tug-of-war, drew tattoos and made drawings, with the Beverly Hills Cop movie soundtrack blasting on the speakers.

In Romania, at the Siret border crossing with Ukraine, women with babies, toddlers and older children continued to arrive, while Romanian firefighters and volunteers welcomed them and carried their luggage to buses transporting them onwards.

The UN is basing its relief plans on four million refugees but has said the figure would likely rise. The European Union is expecting five million to arrive.

Since the start of the invasion on February 24, more than 270,000 people have fled to Hungary, 220,000 to Slovakia and 467,000 to Romania, with most refugees, or 1.85 million, in Poland, according to government and UN data. – Rappler.com