WARSAW - Like many of the exhausted Ukrainians lined up at the concert hall turned refugee center, Lidia Vergun had heard that President Joe Biden arrived in the Polish capital and also that he brought an offer to accept 100,000 Ukrainians into the United States.

She was grateful, she said, but not interested. America was too far.

"I have lived in Ukraine all my life," said Vergun, 52, a grandmother from near Chernihiv who was waiting to collect some of the donated diapers and shampoo being handed out by volunteers. "We want to go back to our motherland as soon as possible."

Vergun's faith that war in Ukraine would be a short-term affair was common among those still reeling from their rush to escape. For now, staying in Poland or other neighboring countries offered their best hope of resuming normal life as soon as possible. Not many Ukrainians in Warsaw have expressed a wish to go beyond the bounds of Poland or surrounding Europe.

"Mostly they are asking to travel to Italy, Germany, Spain. We've only had a few ask about the U.S.," said Rostyslaw Sydoruk, one of the agents registering new arrivals at the center, which has processed more than 10,000 Ukrainian refugees.

Most want to stay in Poland, he said, which shares a 300-mile border with their home country. But many have also boarded the buses and trains that offer free passage to other countries within the European Union. Several refugee workers said they were aware of no free flights from Poland to the United States.

Whether Biden's announcement would open new high-volume paths across the Atlantic for Ukrainians remained unclear Friday. White House officials said the new initiative would channel refugees through a number of existing programs but offered no additional details.

Refugee agencies in Poland said they had not gotten advance notice of the expansion but welcomed any measure that would ease the burden of caring for more than 3.5 million Ukrainians who are on the move.

Christopher Boian, a spokesman for the United Nations High Commissioner for Refugees, called the U.S. announcement "an important demonstration of solidarity not just with the refugees fleeing Ukraine, but with the European countries that have already received millions of them."

But "for the details of how this commitment will be implemented, you need to speak to the U.S. government," he said.

Refugee workers said it was typical for recent refugees to focus at first on the possibility that they would be able to return quickly to their lives. But should the war drag on, more Ukrainians would seize on the chance to seek a haven in the United States, they said.

Many Americans have said they are ready to help Ukrainians if they come. Refugee workers said they are hearing from hundreds of U.S. citizens asking how they can host Ukrainians.

One of them was retired Californian physician Muthiyaliah Babu, who emigrated from India in the 1950s and contacted the United Nations to be part of his adopted country's response to the Ukraine war. He and his wife agreed they could easily accommodate a small family in their Santa Barbara home.

"They told me most of them wanted to stay in Poland, which I understand if they really have a chance of going home," Babu said. "But if they are going to let them in, we are ready to help."

As word of the U.S. offer spread through pockets of Ukrainian refugees throughout the Polish capital, it was met with both excitement and skepticism. Many Ukrainians have tried without success to immigrate through regular channels to the United States for years. They were dubious that the barriers would drop.

"A lot of people don't believe it's true," Olena Bessarabchuk, said of the possibility of a fast track to North America. "It's always been so hard to get a visa for America."

Bessarabchuk, who traveled from Odessa, Ukraine, with four family members and a dog, had lined up for hours outside of Warsaw's main soccer stadium to be registered to work and receive benefits in Poland. She is among the many Ukrainians who plan to wait out the war here.

Yana Khomotiuk, in the same crowd, was keen to reach the United States but skeptical that the new program would benefit her. In the early days of the war, she said, she applied for a visa through the U.S. Embassy in Kyiv but was turned down, despite having relatives in Oregon.

"I want to go there; I have to go there," she said, rolling her baby carriage back and forth to keep her infant asleep. "I can't stay in Poland forever."

But for the young mother whose husband was at home fighting a war, not even the possibility of a path to America was much comfort. With her eyes filling with tears, Khomotiuk seemed to reach the limits of optimism.

"For me, hope or no hope, it doesn't matter," she said. "I have no place to go."

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Julia Alekseeva contributed to this report