Photos and videos show long waits on both sides of border crossings as thousands leave Ukraine

More than 677,000 people have crossed into neighboring countries since the start of the conflict, United Nations high commissioner for refugees Filippo Grandi said Tuesday, making it the largest exodus in Europe since the Balkan wars in the 1990s. More than half have gone to Poland, and people are also streaming into Moldova, Slovakia, Romania and Hungary.

People continue to stream across the borders after long waits over the weekend. Traffic data from Google showed severe backups at nearly every border crossing Sunday at 10:25 p.m. local time, particularly at crossings into Poland. Google has since temporarily disabled live traffic data in Ukraine, amid fears for the safety of local communities. Ukrainians trying to leave by train and bus also struggled with crowds and service halts.

Officials warn that the flow of refugees is likely to escalate into a full-blown humanitarian crisis.

“The situation looks set to become Europe’s largest refugee crisis this century,” said a spokesperson for the UN Refugee Agency UNHCR.

On Sunday, Ylva Johansson, the European Union’s home affairs commissioner, said member nations need to be prepared to support “millions” of Ukrainians in the coming months.

Ukrainians can stay, visa-free, for 90 days in E.U. nations, and Johansson said the E.U. would ask member nations to grant asylum to Ukrainians coming to Europe for up to three years.

Grandi, the U.N. high commissioner for refugees, said Monday at a meeting of the Security Council that if the fighting continues, there could be as many as 4 million refugees — roughly 10 percent of the Ukrainian population — in the coming weeks.

If that scale of exodus holds, this will be Europe’s worst humanitarian emergency since 2015, when more than 1 million people were displaced from Syria, Iraq and Afghanistan.

“The tidal waves of suffering this war will cause are unthinkable,” U.S. Ambassador to the United Nations Linda Thomas-Greenfield said on Feb 23.

More than 410,000 people had crossed into Poland as of Tuesday, according to the country’s border guard. In total, the country is expected to receive up to 1 million refugees.

On Sunday, lines of cars stretched for 20 miles from the border crossing into Medyka, Poland, one of the busiest crossings between the two countries.

Slovakia declared a state of emergency Saturday morning because of the mass influx of refugees caused by the war. The government approved an infrastructure bill of 13 million euros ($14.5 million) to strengthen the Ukrainian border infrastructure and complete asylum facilities.

Nearly 100,000 Ukrainians have crossed into Hungary, according to border police.

Satellite images provided by Maxar showed a four-mile-long line at the border crossing in Siret, Romania, on Friday. Romania’s border police said some 105,000 Ukrainian citizens crossed the border in the first five days of the conflict. The Romanian defense minister said earlier that the NATO country of 19 million could take in up to 500,000 refugees.

Moldova’s border police said Monday that nearly 70,000 Ukrainian citizens had entered the country since Feb. 24, with the largest flows coming from the Criva and Palanca crossings.

As conflict intensified, Ukraine’s border guards were ordered Friday to stop all male citizens between the ages of 18 and 60 from leaving the country, disappointing many who got to border checkpoints after hours of travel and wait.

“If I could go, too, I would,” Vitali, 31, told The Washington Post after his wife and child crossed into Poland, with tears in his eyes. “It’s brutal.”

Annabelle Timsit, Leslie Shapiro, Monica Ulmanu, Shelly Tan and Youjin Shin contributed to this report.