MUNICH -- Embracing its role as a defender of those in need, Germany welcomed at least 10,000 more asylum seekers into the country Saturday. As officials worked to give all a firm roof over their weary heads, a packed stadium cheered some of the littlest newcomers, who walked in hand-in-hand with top soccer players.

Germany over the past week has taken in more than 40,000 people fleeing war and poverty in the Middle East, Asia and Africa -- and a poll has suggested broad support for the government's course.

Still, Vice Chancellor Sigmar Gabriel said the sheer speed of arrivals was outpacing Germany's ability to provide emergency housing. He said Germany needed its European Union partners to agree to host some of the newcomers at a meeting Monday in Brussels. Several Eastern European nations have insisted they won't accept any EU quotas on taking asylum seekers.

"Because of the speed at which large numbers of people are coming in, Germany is approaching a situation where we are reaching our limits," Gabriel said.

Front-line aid workers said Germany was determined to meet the challenge and provide as warm a welcome as possible. The country's biggest soccer club, Bayern Munich, took the field Saturday with each player holding a newly arrived child by the hand. Some 75,000 fans roared their approval as many of the kids waved shyly back.

"Munich is doing the right thing. We have to help them," said Johann Hoerterer, a bus driver waiting at the city's central train station to ferry newcomers to refugee shelters across Bavaria.

"It is a positive experience for me. It's not fun for anyone, but they've fled war and bombs. If it were me, I'd do the same -- get away to security," said Hoerterer, standing before a new row of tents at the station providing medical care, food, clothes and other support.

"But these people need to be taken in by the whole of Europe, not just here in Germany," he added.

Some 450,000 migrants have arrived in Germany this year. The country is expecting at least 800,000 in 2015 -- by far the most in the 28-nation EU.

Chancellor Angela Merkel is facing some criticism from Bavaria's governing party, the Christian Social Union, the sister party to Merkel's own conservative Christian Democrats.

Bavaria's governor, Christian Social Union leader Horst Seehofer, was quoted as telling the weekly Der Spiegel that Germany's Sept. 5 decision to open its borders to migrants stuck in Hungary was "a mistake that will occupy us for a long time." Seehofer said he sees "no possibility of getting the cap back on the bottle."

Merkel on Saturday countered that her coalition government "made a decision last week in an emergency situation ... and I am convinced that it was right.'

As Germany hoped to make the end of the migrants' journey positive, tragedy continued to strike other links in the epic chain that leads from Syria to Turkey, through Greece and the Balkans, to Hungary and on to northern European nations

Greece's coast guard said it was searching Saturday for four children aged 8 to 13 and a 20-year-old man who disappeared when two boats carrying 61 people from Turkey to the islands of Samos and Lesbos overturned in the Aegean Sea. Scores have drowned over the past year on that route, even though the sea crossing is relatively short.

Greek police said about 3,500 more crossed the country's northern border into Macedonia, while Austrian police said more than 6,000 walked across the Hungarian border to the border town of Nickelsdorf, where fleets of buses whisked them to several Austrian towns and cities for onward travel to Germany. Scores of taxis also waited at a nearby gas station offering people rides to Vienna for 150 euros ($170), sharply higher than the usual rate.

Hungary's prime minister, Viktor Orban, proposed that the European Union step up aid to Syria's neighbours to stem the flow of refugees from camps there, and declared there is "no fundamental right to a better life."

Munich has been the main point of entry for migrants reaching Germany. City officials said they might need to start erecting big tents to house some arrivals.

Upper Bavaria's regional government said at least 10,000 and possibly up to 13,000 people were expected Saturday in Munich, the main hub for migrants to reach Germany, following Friday's total of 5,800 arrivals. At least two special trains were carrying migrants to Germany's northern states.

Rwanda Seraj, a Syrian-born woman greeting newly arrived asylum seekers at Munich's train station, said the flow of people had been intense all week.

"I haven't slept much in the past few days but I don't realize the time. Suddenly it's night time," said Seraj, who arrived from Syria 2 1/2 years ago and is studying pharmacy in Munich. "I see it as my responsibility to help the people fleeing."

"When they arrive, they immediately want to see someone, or hear something, that is familiar. They quickly realize I come from Syria, they see my headscarf, and they come to me," Seraj said. "They ask: 'Where are we? Which city? Which state? Where are we going? Can we go to Sweden?"'

Germany and Austria have stressed the right to asylum for war refugees but Hungary has argued that most are economic migrants seeking better jobs and therefore not entitled to stay in the EU. Hungary and other eastern nations such as the Czech Republic and Poland have rejected proposed quotas to spread the human tide around the 28-nation union.

Hungary plans to start enforcing tougher security on its border with Serbia starting Tuesday. Asked by the German daily Bild where future arrivals should go, Orban replied, "To where they came from."

He argued that people coming to Europe from camps in Lebanon, Jordan and Turkey "were safe there."

"There is no fundamental right to a better life, only a right to safety and human dignity," Orban declared.

Orban suggested every EU country pay 1 per cent extra into the EU budget to provide aid to countries bordering Syria that host refugee camps. He said this would generate 3 billion euros ($3.4 billion) for aid.

But Germany's commissioner for immigration, refugees and integration, Aydan Ozoguz, said Orban was being "extremely cynical" to describe refugee camps bordering Syria as safe environments. She cited World Food Program decisions to slash food rations to refugees in Jordan and Lebanon as indicative of deeper problems there.

"Everyone who has been following this knows that the food rations there have been halved. One really can't speak of safety," Ozoguz said on Germany's rbb-Inforadio.

Saudi Arabia, which along with other oil-rich Gulf states has faced repeated calls to shelter more Syrian refugees, responded Saturday by saying it has taken in about 2.5 million Syrians during that nation's four years of civil war. Saudi Arabia never before had given any figure.

The official Saudi Press Agency quoted an unidentified official at the Foreign Ministry saying the kingdom does not consider those taken in as refugees and does not house them in camps "in order to ensure their dignity and safety."

The statement said "hundreds of thousands" had received Saudi residency, but didn't specify how many of the total 2.5 million are currently in the country.

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Moulson reported from Berlin. Associated Press reporters Mstyslav Chernov and Philipp-Moritz Jenne in Nickelsdorf, Austria; Pablo Gorondi, Shawn Pogatchnik and Dimitri Kozlov in Budapest; Balint Szlanko in Roszke, Hungary; Adam Schreck in Dubai, United Arab Emirates; and Demetris Nellas in Athens, Greece, contributed to this report.