CHICAGO (NewsNation) — Thousands more refugees crossed into Eastern Europe Friday as the conflict in Ukraine entered its fourth week.

At least 3.2 million have fled abroad, according to United Nations data, in what has become Europe’s fastest-growing refugee crisis since World War II.

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.

In Poland, more than 2 million refugees have entered since the start of the Russian invasion, the Polish border guard said on Friday.

More than 197,000 refugees have registered with authorities so far in Germany, an interior ministry spokesperson said on Friday. In Spain, that number is 4,500, and in Norway, which is not in the EU but is also granting collective protection, 2,000. 

While refugees have fled to nearby counties, many wonder how difficult getting them to the United States is. The Biden administration has authorized $1B in humanitarian financial aid, provided temporary protected status to thousands of Ukrainians already in the U.S. and temporarily halted deportations to Ukraine.

Yet, despite President Joe Biden tweeting, “We will welcome Ukrainian refugees with open arms,” that hasn’t quite happened.

Ukrainian refugees can’t enter the U.S. without a visa, but the U.S. embassy in Ukraine is closed due to the war.

Once they’re in any other European country, they can go to the U.S. Embassy and apply for refugee status; however, that process could take years to complete.

Some family members have tried to get their loved ones tourist visas, which is a much faster process, but refugees must prove that they will leave after a short visit, which is hard to do with your country at war.

Another option within the immigration system is humanitarian parole, which allows anyone with a compelling emergency to temporarily enter the U.S. on a case-by-case basis. Anyone can apply.

Meanwhile, it’s not just Ukrainians trying to flee their homeland; many Russians are undergoing a similar process to try and flee Russia as the nation becomes more autocratic. Some Russians pay thousands of dollars for a single flight to get out, then test their luck applying as a refugee at an American consulate in a foreign nation. 

Reuters contributed to this report.