BERLIN — A top German official said his country could take half a million refugees a year "for several years," even as some critics questioned Tuesday whether generous asylum policies serve to entice more migrants to make the dangerous trek toward Western Europe.

"I believe we could surely deal with something in the order of half a million for several years," Vice Chancellor Sigmar Gabriel told broadcaster ZDF late Monday night.

He spoke amid signs that the migrant flow — many from war-battered Iraq and Syria — is only escalating amid a humanitarian crisis that has sharply tested European cooperation and fundamental policies such as open borders.

A ship crammed with thousands of migrants docked in the Greek port of Piraeus near Athens. Greek authorities, meanwhile, rushed to send help to the island of Lesbos off the Turkish coast, where 20,000 migrants have been growing increasingly frustrated by the long wait in squalid conditions for a ferry to the mainland.

Further up the route traveled by the majority of migrants entering the continent, a record 7,000 Syrians reached the Greek border with Macedonia, the U.N. refugee agency reported Tuesday. Greek television broadcast chaotic scenes as migrants struggled to cross the border.

And on the border between Hungary and Serbia, migrants slept in an open field after clashing with police the day before. Hungarian Prime Minister Viktor Orban, who ousted his defense minister late Monday over a missed deadline for building a border fence, told the newspaper Magyar Idok that the government would speed up construction.

Gabriel said other European nations needed to do more to address the crisis, even as Britain and France — two nations criticized for not doing enough — pledged to take in tens of thousands of asylum-seekers.

Germany — the nation taking in the lion's share, an estimated 800,000 by year's end — has continued to lead the way. The government pledged Monday to hire 3,000 more police officers and spend $6.7 billion more to address the crisis, including emergency housing for 150,000 people.

Yet even as German Chancellor Angela Merkel said her nation should be proud of its response, other European leaders and domestic critics blamed Germany — as well as similarly generous nations such as Sweden — for offering benefits so lucrative that they had become an incentive for asylum-seekers to risk their lives over land and sea.

Germany responded to the criticism Monday by announcing a reduction in cash handouts for asylum-seekers during their initial months of processing, instead saying it would offer them more food stamps and inkind aid.

Berlin also said it would push to have western Balkan countries such as Kosovo declared "safe" in a bid to weed out the many thousands of migrants now claiming asylum from countries not at war.

The German maneuvers reflected the complex nature of Europe's migrant crisis, in which desperate Syrians and Iraqis are searching for sanctuary in the wealthy countries of Europe's core along with a host of economic migrants pouring in from countries as far-flung as Pakistan and Bangladesh.

"We want to reduce the number of pull factors, and I think it's a big step forward that we have consensus in our government to reduce the monetary benefits for those seeking asylum," said Stephan Mayer, a German national lawmaker and home affairs spokesman for the Christian Social Union, part of Merkel's ruling coalition.

In the crowded refugee centers across this nation of 81 million people, asylum-seekers have conceded that they have come to Germany because it is doing more to help than other nations in the region.

Mohammed Mazher Alkilany, 28, a former PR consultant for the Damascus tourism board who is living in a temporary shelter in east Berlin, said his family of three is living on 233 euros a month provided by the government — a sum he described as too little to cover the cost of warm clothes and blankets for the coming winter.

But they are also living in free temporary housing in a building outfitted with a playground and rooms with shared kitchens, bathrooms and washing machines. He insisted, though, that he did not come to Germany simply for its generous benefits.

"I came here because Germany is safe; there is no war," he said. "Germany is the best in Europe. France is no good, you cannot get language classes there, but in Germany, you can learn the language for free."

Hungarian camerawoman trips refugees running from police

When dozens of refugees tried to escape from police officers at a Hungarian camp on Tuesday, one camerawoman decided to get involved. While she was filming a father, holding a child in his arms, she tripped both of them.

The scene at the Roeszke camp was captured by a German correspondent. According to Hungarian news site 444.hu, the camerawoman worked for Hungarian broadcaster N1 and has since been fired.

On its website, the TV station posted a statement that read: "Today, a N1TV colleague behaved unacceptably at the Roeszke reception center. The cameraman's employment was terminated with immediate effect." The statement was signed by N1TV editor Szabolcs Kisber. On its website, the channel describes itself as being "fact-based" and "free of opinion."— The Washington Post

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