A migrant holds a child while trying to enter a train Saturday at a station in Tovarnik, Croatia. (Antonio Bronic/Reuters)

Thousands of asylum seekers stranded in Croatia began to pour into neighboring Hungary and Slovenia on Saturday as the stop-start mass migration across Europe continued, escorted out of the Balkans by rows of police in riot gear, watched over by circling helicopters and Humvees with mounted guns.

More than 20,000 war refugees and economic migrants from the Middle East and beyond awoke Saturday morning in Croatia having spent the night huddled in train stations, parking lots and rough camps alongside rivers.

They were uncertain when or where they would be permitted to continue their trek. Hundreds crowded onto a bridge over the Sava River, their passage blocked by Slovenian police. At a nearby checkpoint on the highway at Bregana, thousands more were penned into a waiting area alongside the highway.

Slowly, a bus load at a time, the migrants were permitted to enter Slovenia, one step closer to their ultimate destinations in Germany and Scandinavia.

“They took us here, but they have not promised anything,” said Hussein, 40, who in a past life managed a shoe factory in Aleppo in northern Syria.

He was standing in front of a green canvas tent behind a Slovenian police station. Hussein, who withheld his full name, was separated from his wife two hours earlier. She was taken to a different processing center. He hoped to be reunited with her soon. Not only was she carrying his passport, she was also pregnant.

Slovenian Prime Minister Miro Cerar toured the processing center and spoke briefly with The Washington Post. Cerar said that the refugees would be allowed to continue their journeys soon, but he would not say when. He emphasized that Slovenia had not shut its borders.

“We’re not closing borders, we are enforcing border controls,” Cerar said. “We’ve prevented a mass influx.”

Slovenia will bring the migrants into processing centers in a careful, orderly fashion, he said. They will be quickly registered and offered food, shelter and medical care. “We will see what our capacities are,” Cerar said.

Asked if the refugees and migrants would eventually be allowed to leave for Austria and Germany, the prime minister said they would. But he lashed out at the Croatian government for creating a crisis.

“It was a complete disaster,” he said of the Croatian decision to allow refugees to race across their borders and then panic by pushing the same migrants quickly toward Slovenia and Hungary.

“It was very irresponsible,” Cerar said.

Slovenia wasn’t alone in complaining about Croatia.

On Friday night, as many as 1,000 asylum seekers were shipped from Croatia to Hungary on a special train, accompanied by 36 Croatian police. This move was answered by howls of protest from Hungarian officials who accused Croatia of abetting human trafficking.

Hungarian government spokesman Zoltan Kovacs said the move to shove asylum seekers toward Hungary showed “the Croatian system for handling migrants and refugees has collapsed, basically in one day.”

“What we see today is a complete failure of the Croatian state to handle migration issues,” he told Sky News.

Croatian authorities were not only allowing migrants to cross their border to Hungary at the town of Beremend, but they were also paving the way.

In a highly orchestrated transfer that involved clear coordination between the two countries’ authorities, dozens of buses waited for hours on the Hungarian side of the border on Saturday to receive the arrivals from Croatia amid a heavy police presence.

While aid agencies organized pallets of water, diapers, baby food and snack bars for the arrivals, locals from Beremend arrived with pots of goulash and home-baked cakes for the scores of police officers awaiting the surge.

There was also a military component that was extraordinary for a border between two European Union countries. Three military Humvees armed with 12.7mm guns waited in the transit zone, while soldiers in body armor and carrying riot shields marched into the area as the first buses of refugees arrived.

Bus after bus arrived from Croatia, unloading refugees who were tired but elated to be making progress toward Germany, their goal.

“We took a risk. It was a very difficult crossing, the waves were very high, but staying at home is more dangerous than making this journey,” said Nawaf, a teacher from northeast Syria who had been traveling for eight days with his wife, Maha, and their 1-year-old daughter, Sara.

The last few days involved crisscrossing Serbia and Croatia as borders opened and shut without notice. They were sleeping rough when they were picked up by Croatian authorities and brought to the border.

“All we want is peace and freedom. We are so liberal. We just want to get to Germany and stay and work in Germany,” said Nawaf as he sat in a sweltering bus to ride into the Hungarian transfer zone.

They did not know where they were going.

Later, the same refugees were spotted at the nearest train station. Police there said they would travel by train to the Austrian border. The refugees waved and smiled as they saw familiar reporters.

“No one told us where we are going or what we are doing,” said Said, a 23-year-old English major from Damascus University, as he came off one of the buses to board a train at the Magyarboly station. “They’re just telling us to line up, go here, get on this bus, like we are uncivilized people, but we are not uncivilized people. We just want to do well.”

Said nevertheless had a huge smile across his face as word spread that they were being taken to the Austrian border.

Croatian leaders said their intent has been to treat the refugees with humanity, and many migrants say they have been warmly received, even if sometimes their hosts didn’t seem to know what they were doing.

Croatia has staggered under the weight of the influx after initially opening its arms to the refugees. The prime minister warned that the nation of
4.2 million could handle no more. But locals came out to help in spontaneous shows of generosity.

Mirela Majetich and her daughter dropped off an Iraqi family at a border bridge, seeing them off with a group photograph and some tears.

“We saw them with sick babies. Mothers. Pregnant women. It is heartbreaking, and we are not made of stone. We had to do something,” said Majetich, who works as an administrator in the state court.

She said Croatians remembered when they were the refugees knocking on Europe’s door during the chaos and violence of the Balkan wars two decades ago.

Today’s migrants entered Croatia from Serbia last week, passing close to the city of Vukovar, the scene of a months-long battle that left 2,000 dead in 1991 in some of the worst fighting in Europe since the end of World War II.

The heavily damaged Vukovar water tower, pocked with holes left by shelling, was preserved as a monument. A passerby can see it from miles away, if they know what to look for.

Fifield reported from Beremend, Hungary. Marica Rakicevic contributed to this report.