BERLIN — A growing sense that Afghanistan is slipping into greater chaos and will not stabilise anytime soon is driving rising numbers of Afghans to flee for Europe, hopeful that they will enjoy the same welcome given to Syrians and Iraqis seeking safety from war and terror.

Aided by smugglers, and worried that borders would soon close along the migrant trail through the Balkans, about 64,000 Afghans were registered entering Greece last month, according to the UN High Commissioner for Refugees, second only to Syrians and more than double the 27,500 who were registered the month before.

On a recent morning on the Greek island of Lesbos, a black rubber dinghy slid gently onto shore in the first light, and Hadi Atti, 17, a baby-faced high school student from a village outside Kabul, the Afghan capital, shouted, “We are here, we are here!”

Atti said the crossing from Turkey was smooth but very cold. “But we made it, and now we can continue on,” he said.

Where to? “Germany!” several of his travel companions shouted. “Austria,” one man said. “I will go to Sweden,” Atti said.

But after a month of harrowing travel, rushing to reach Central and Northern Europe before more borders are closed, the Afghan migrants may be facing a new obstacle to their dreams of safety and security: A hardening stance by the German government on who gets to stay for a year, or more.

German officials argue that Afghanistan is not universally unsafe, so not all migrants should be granted asylum. The interior minister, Mr Thomas de Maizire, has said that applicants would be judged on a case-by-case basis, adding that “not all of the people who come to us as refugees from Afghanistan can expect to stay in Germany”.

Officials in Germany also note that the country has had troops in Afghanistan for 14 years and has poured more than 2 billion euros (about S$3.05 billion) into civilian projects. Chancellor Angela Merkel has suggested that those efforts fulfil Germany’s commitment to care for those in need, meaning it should not necessarily have to shelter Afghans in Germany, too.

That tougher stance by Germany is emerging as the biggest test case yet of Central and Northern Europe’s willingness to absorb people from the world’s most troubled regions. At the same time, it may force a debate over who qualifies as a refugee.

“Life in Afghanistan is worsening and the fighting is increasing,” Atti said. “There is the Taliban. There is ISIS. It is very bad,” he added, referring to the militant group also known as the Islamic State or ISIL.

Germany’s own foreign ministry “urgently warns” against travel to Afghanistan.

Ms Melissa Fleming, spokeswoman for the UN refugee agency, said some of the Afghan migrants might be leaving for a better life in Europe’s most prosperous countries, but for many, “it is well documented that these are extremely dangerous situations” that they face living in Afghanistan, one of the poorest countries on earth.

At the same time, Afghanistan’s sophisticated networks of smugglers appear to have accelerated their operations, capitalising on growing fears over advances by the Taliban, and inroads by the Islamic State.

About 67,000 Afghans have entered Germany seeking asylum this year — almost half of them last month alone, officials said. Mr De Maizire has said that the arrival of so many members of Afghanistan’s middle class was “unacceptable”.

“We are in agreement with the Afghan government,” he said, of concerns that Afghanistan’s population would be depleted of future leaders. “We do not want that.”

Afghan migrants in Germany said they were already feeling the effects of the government’s harder line.

Mr Sayed Aliraza, 24, was among the thousands of new arrivals waiting in Berlin’s main migrant reception centre, hoping to appeal what he said had been his rejection from German-language classes.

Mr Aliraza said he had broken off his studies of law and politics in his third year at Kabul University and left for Europe in April with his parents, brother, sister-in-law and their five children.

He said he was in his third day of seeking redress from a Berlin bureaucracy severely strained by the migrant influx, to present a paper he said showed approval to start the classes. He said the government, which insists newcomers learn German, was no longer helping Afghans.

“I think the German government does not want for Afghan people to learn Deutsch,” he said. “I understand — the government of Germany doesn’t have place for refugees. But we are also human.”

“We don’t have any security there,” he added, referring to Afghanistan. “That is the reality. Afghanistan is not secure, and the government of Germany knows this.”

Germany is balking at looking after Afghans on both ends. Since German troops were first deployed to Afghanistan in 2001, in post-9/11 solidarity with the United States, 54 German soldiers have been killed, the biggest toll of any German deployment abroad since 1945.

Noting that American, German and other forces will now stay beyond 2016, Ms Merkel has argued that that commitment — plus more aid — can give Afghans “more possibility to build up their country”.

Mr Mohamed al Zoda, 20, a Hazara from Baghlan province at the main migrant centre in Berlin, said he did not buy Ms Merkel’s argument.

“The case here is that our government is bribed,” he said, sitting among a group of young Afghan men at the centre last week. “They are not good guys.”

“Foreign countries give aid,” he added, but the government “gets the money and put it in their pocket”.

“They do not have any solutions for people,” he said. NEW YORK TIMES