Pope Francis has called on every European parish, religious community, monastery and sanctuary to take in one refugee family, as thousands of people from war-torn countries continued to stream into Germany via Austria.
The pope said on Sunday the Vatican would open its doors to two refugee families, but provided few details as he addressed tens of thousands of people in St Peter's Square.
Francis said it was not enough to say, "Have courage, hang in there," to the hundreds of thousands of refugees who are on the march towards what he called "life's hope".
He called on every Catholic parish, convent, monastery and sanctuary in Europe to shelter a family, and asked bishops throughout Europe to urge their dioceses to do the same.
His comments came after about 8,000 refugees arrived in Munich over the past two days, with a further 8,000 expected to arrive on Sunday.
They seemed dazed by the calls of "Welcome to Munich", from the few dozen well-wishers remaining at around midnight, as well as by their determination to thrust chocolate bars, bananas or bread rolls into their hands.
Whoever still thinks that withdrawal from the EU or a barbed wire fence around Austria will solve the problem is wrong.
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Many of the refugees said they were fleeing the civil war in Syria, while others were from Afghanistan or Iraq.
German interior ministry spokesman Harald Neymanns said Berlin's decision to open its borders to Syrians was an exceptional case for humanitarian reasons. He said Europe's so-called Dublin rules, which require people to apply for asylum in the first EU country they enter, had not been suspended.
"The Dublin rules are still valid and we expect other European Union member states to stick to them," he said.
After days of confrontation and chaos, Hungary deployed more than 100 buses overnight to take thousands of the refugees who had streamed there from southeast Europe to the Austrian frontier. Austria said it had agreed with Germany to allow the refugees access, waiving the asylum rules.
"Every refugee I spoke to was glad they left the horrendous experience they said they had in Hungary these past few days," Al Jazeera's Mohammed Jamjoom, reporting from the Austrian town of Nickelsdorf, said.
"People here were provided with clothing, blankets and tents," he said.
Hungary, the main entry point into Europe's borderless Schengen zone for refugees, has taken a hard-line, vowing to seal its southern frontier with a new, high fence by September 15.
Hungarian officials have portrayed the crisis as a defence of Europe's prosperity, identity and "Christian values" against an influx of mainly Muslim refugees.
Budapest has been heavily criticised for its position, but the country's foreign minister, Peter Szijjarto, said Hungary should not be blamed for adhering to the EU rules.
A "failed migration policy of the European Union" and "the series of some irresponsible statements made by European politicians" were to blame for the crisis, Szijjarto said.
EU foreign ministers met in Luxembourg on Saturday to brainstorm possible solutions, but the usual diplomatic conviviality unravelled as they failed to agree on any practical steps out of the crisis.
Ministers were especially at odds over proposals for country-by-country quotas to take in asylum seekers.
"Given the challenges facing our German friends as well, all of Europe needs to wake up," Austrian Interior Minister Johanna Mikl-Leitner said.
"Whoever still thinks that withdrawal from the EU or a barbed wire fence around Austria will solve the problem is wrong."
British Finance Minister George Osborne said Europe and the UK must offer asylum to those genuinely fleeing persecution, but must also boost aid, defeat people-smuggling gangs and tackle the Syrian conflict to ease the crisis.
Austrian Chancellor Werner Faymann called on Sunday for an emergency EU summit to resolve the refugee crisis, saying his country's admittance of thousands of refugees crossing from Hungary was just a "temporary" measure.
Pressure to take effective action rose sharply this week after pictures flashed around the world of a drowned three-year-old Syrian-Kurdish boy, Aylan Kurdi, washed up on the beach of a Turkish resort, personalising the collective tragedy of the refugees.
Source: Al Jazeera and agencies