ATHENS, Greece — Disasters at sea claimed the lives of dozens of migrants on Sunday, as desperate people fleeing war and poverty braved the risky journey to seek sanctuary in Europe.

Thirteen migrants died after their boat collided with a ferry off the Turkish coast, officials there said, while the Greek coast guard fanned out in the choppy waters of the Aegean Sea searching for another 24 people missing after their boat sank off the island of Lesbos.

Coast guard officials said nearly three dozen people were rescued in the two incidents, which followed another sinking near Lesbos Saturday, in which a 5-year-old girl drowned. Two bodies were found in Greek waters, but authorities aren’t yet sure which shipwreck killed them.

The events highlight the risks that those fleeing the Middle East, Africa and Asia are willing to take in hopes of reaching sanctuary in Europe. Men, women and children continue to take the perilous sea journey despite the fact that thousands of earlier migrants find themselves blocked by closed border crossings in the Balkans.

Hungary’s decision to shut its border with Serbia on Sept. 15 set off a chain reaction in Croatia and Slovenia that has forced people fleeing violence in their homelands to rush from one European border to the next as they desperately try to find their way north before the rules change again.

Thousands are on the move all over southeastern Europe as authorities struggle to respond. About 15,000 migrants crossed into Austria from Hungary and Croatia over the weekend.

Hungary erected yet another steel barrier, now at Beremend border post with Croatia, complete with a giant steel door to control the flow of migrants. The gate slowed the flow. But they just kept coming.

In the Austrian border village of Nickelsdorf, people arrived by foot after completing a half-an-hour walk from the Hungarian town of Hegyeshalom. From there, buses and trains take them to emergency shelters in Vienna and other parts of Austria.

The asylum seekers lined up, waiting for buses to relocate them across the country. Austrian soldiers stood alongside. Local officials struggled to find them places to stay, since many camps across Austria are already overcrowded.

Mahat, a lab technician from Damascus, was one of the thousands waiting to get onto the buses.

“We came here only to get a new life,” said Mahat, who didn’t want to give his last name fearing repercussions by the Syrian government.

The 47-year-old said he had been trekking through Croatia with another 5,000 people before he eventually made his way to Nickelsdorf. He said he didn’t care where in Europe he would end up as long as he could live in peace and find a job.

Mahat said he was originally living and working with his family in the United Arab Emirates until his father died in Syria three years ago.

“I came to Syria to put my father in the ground. Then the government took my passport and they cut it. So three years I was suffering inside,” he said. “When I got the chance I just ran away and came here.”

Conditions along the borders worsened, as days of intense heat gave way to rain and plummeting temperatures. Along the border in the Croatian town of Tovarnik, volunteers handed out tents and warm clothes

“Unfortunately we sleep here on the ground without anything. It was very cold,” Muhammad Dakiri, a Syrian migrant, said. “Suddenly the weather has turned to cold and raining. We couldn’t sleep well because in an hour or half an hour we wake up because we’re feeling cold.”

Meanwhile, leaders all across the region are sniping at one another, underscoring the sense of crisis and disarray in the days before European leaders meet to discuss the crisis.

Hungary’s erection of razor-wire fences is deeply straining its ties with neighboring countries, who feel the problem of the huge flow of migrants is being unfairly pushed onto them. After completing a fence along the border with Serbia, Hungary is now building fences along its borders with Croatia and Romania.

After lashing out against Croatian officials, Hungarian Foreign Minister Peter Szijjarto is now trading barbs with his Romanian counterpart over the fence.

Romanian Foreign Minister Bogdan Aurescu on Saturday called the border closure an “autistic and unacceptable act” that violated the spirit of the European Union.

“We would expect more modesty from a foreign minister whose prime minister is currently facing trial,” Szijjarto said. That was a reference to corruption charges filed recently against Romanian Prime Minister Victor Ponta.

“We are a state that is more than 1,000 years old that throughout its history has had to defend not only itself, but Europe as well many times,” Szijjarto added. “That’s the way it’s going to be now, whether the Romanian foreign minister likes it or not.”

The Hungarian Foreign Ministry has called in the Romanian ambassador for a consultation on Monday.

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