The huge influx of migrants into southern Germany has continued unabated, with the Munich police reporting 12,200 arrived on Saturday.
But the city authorities have again warned they are at “the limit” when it comes to coping with the numbers.
“We have reached the upper limit of our capacity,” a police spokesman said, as frantic efforts were under way to accommodate the new arrivals.
Record numbers have also been crossing from Serbia into Hungary.
More than 4,000 people walked across the border with Serbia – the most so far in one day – just as the authorities in Hungary were completing preparations to seal the frontier.
Europe as a whole is struggling to deal with an enormous influx of people, mostly from Syria but also Afghanistan, Eritrea and other countries, fleeing violence and poverty.
Munich, in Germany’s southern state of Bavaria, has been the main entry point for those entering the country in search of a better life, but the city says it is having difficulty finding accommodation for them.
“We lack 1,000 to 5,000 places,” Munich Mayor Dieter Reiter told theSueddeutsche Zeitung (in German).
The authorities are considering using a sports venue from the 1972 Olympics, the Olympiahalle, as a temporary shelter.
Mr Dieter also repeated his call for other German regions to take in more migrants.
Germany’s Chancellor Angela Merkel has defended the decision to let in large numbers of refugees, saying she was “convinced it was right”.
A steady stream of migrants stretches from Greece, through Macedonia, Serbia and Hungary, to Austria and Germany. Many crossed the sea in little more than play boats from Turkey to several Greek islands.
Officials estimate that 175,000 migrants have crossed from Serbia into Hungary so far this year.
Hungarian Prime Minister Viktor Orban has promised to seal the country’s borders and arrest any illegal migrants. The country is close to finishing a 4m-high (13ft) fence along the border with Serbia.
More than 4,000 Hungarian soldiers have been brought in to help police enforce a ban which Mr Orban has ordered must come into effect on Tuesday.
The BBC’s Nick Thorpe – reporting from Szeged near the Hungarian-Serbian border – says the humanitarian infrastructure to deal with the migrants is finally being established at the Roske migrant camp.
On Friday, footage emerged of migrants being thrown bags of food at the camp amid criticism that they were being treated like animals.
On Saturday, Austrian Chancellor Werner Faymann drew parallels between Hungary’s treatment of refugees and Nazi Germany’s treatment of Jews.
In response, Hungarian Foreign Minister Peter Szijjarto said Mr Faymann’s comments were “slanderous”.
The 4,000 refugees who walked into Hungary on Saturday were shepherded into a field where dozens of large tents, including those of the UN refugee agency, now stand.
Most migrants want to travel on to western Europe by passing through neighbouring Austria, but before they do so, the Hungarian authorities say that it is necessary to transport them to camps so that they can be registered.
The European Commission has announced plans last week for mandatory quotas to share out 120,000 additional asylum seekers among 25 member countries.
Tens of thousands of people took part in a “day of action” on Saturday in several European cities – and in Australia – in support of refugees and migrants. Some cities also saw counter-demonstrations.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.