Thousands more migrants streamed into Germany on Sunday, greeted with cheers and "welcome" signs, as Pope Francis called on every Catholic parish in Europe to take in a refugee family.
In moving scenes, the newcomers clutching their children and sparse belongings stepped off trains to applause from well-wishers who held balloons, snapped photos and gave them water, food and clothes.
German police said they expected a record 10,000 refugees to arrive in the southern state of Bavaria alone by the end of the day.
"The people here treat us so well, they treat us like real human beings, not like in Syria," said Mohammad, 32, from the devastated town of Qusayr, his eyes welling up with tears.
Europe's worst refugee crisis since World War II has exposed a growing east-west rift within the EU, with frontline Hungary -- which first held back migrants, but later sent them on to Austria and Germany -- rejecting the bloc's "failed immigration policy".
Hungary's conservative Prime Minister Viktor Orban, who has sought to secure his country's Serbian border with a fence, has voiced concern about mostly Muslim refugees undermining what he called Europe's Christian identity.
Pope Francis, however, in a Sunday sermon stressed it was Christian to help those in desperate need and urged "every parish, every religious community, every monastery, every sanctuary in Europe" to take in a family.
Turkish police officer Mehmet Ciplak, who was pictured cradling the toddler's body, has recounted how he prayed the little boy was still alive as he walked towards him and scooped him up from the water's edge.
The scale of suffering has led Germany in recent days to drop normal formalities and allow in vastly higher numbers of refugees.
As train and busloads have kept on coming from Hungary, Germany took in another 6,000 people by 1500 GMT Sunday and expected 4,000 more through the day, after about 8,000 refugees arrived on Saturday, police told AFP.
In all, Europe's most populous nation expects 800,000 new asylum applications this year -- four times last year's total and more than any other EU nation -- at an estimated cost to the state of 10 billion euros ($11 billion).
As refugees got off trains, police directed them to waiting buses bound for temporary shelters, which have been set up in public buildings, hotels and army barracks across the country.
"Say it loud, say it clear, refugees are welcome here," crowds chanted overnight at the Frankfurt railway station.
In a sign the exodus from Syria shows no sign of abating, rescuers in Cyprus said Sunday they had saved more than 100 refugees fleeing the war after their boat ran into trouble off the eastern Mediterranean island.
"There is no alternative to a common European solution," said Faymann, calling for an EU summit immediately after a September 14 interior ministers' meeting.
Berlin and other capitals have called for binding refugee quotas for each EU country, and common rules on the granting of asylum.
European Commission President Jean-Claude Juncker is expected to present a plan Wednesday to relocate 120,000 refugees from overstretched Italy, Greece and Hungary.
German Chancellor Angela Merkel on Saturday spoke by phone with Hungary's Orban, and both agreed to "meet their European obligations, including their obligations under the Dublin agreement," said her spokesman Georg Streiter.
Under the Dublin rules, asylum applications must be processed by the country where a person first arrives.
Merkel was set to hold a crisis meeting on the refugee issue later Sunday with her coalition partners.