The huge influx of migrants into southern Germany has continued unabated, with the Munich authorities now saying 13,000 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.
As well as the 13,000 who arrived on Saturday, another 1,400 arrived in Munich on Sunday morning, police said.
"We lack 1,000 to 5,000 places," Munich Mayor Dieter Reiter told the Sueddeutsche Zeitung (in German).
The authorities are considering using a sports venue from the 1972 Olympics, the Olympiahalle, as a temporary shelter.
Mr Reiter 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 is travelling 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 people have crossed from Serbia into Hungary so far this year.
Hungary is aiming to complete a four-metre-high (13ft) fence along the border with Serbia by 15 September, when tougher measures, including arresting illegal immigrants, come into force.
The BBC's Nick Thorpe, reporting from Szeged near the Hungarian-Serbian border, says that the humanitarian infrastructure to deal with the migrants is finally being established at the much-criticised 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.
Analysis - Damien McGuinness, BBC News, Berlin
Given the huge numbers arriving in one train station at the same time, it's impressive that almost all of the migrants have so far have been provided with shelter.
But it was only possible, say the authorities, thanks to help from local people, who provided supplies and manpower.
A row is now brewing between the regional state governments, responsible for looking after migrants, and the federal government in Berlin.
The mayor of Munich says he has been left in the lurch by the rest of the country, while other regional government leaders have criticised Chancellor Angela Merkel's recent announcement, that Syrian refugees would be welcome.
The next challenge is to get people from Munich to the rest of Germany. There's a quota system for each region to take in a set number of migrants and refugees.
Deutsche Bahn, the national train network, has announced that some regular trains from Munich will be reserved for migrants and refugees and that passengers who have booked that journey will now have to change to other trains.
It's one of the first concrete signs that taking in so many people will have an impact on the lives of ordinary Germans.
Read more BBC coverage of the migrant crisis
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 announced plans last week for mandatory quotas to share out 120,000 additional asylum seekers among 25 member countries.
Hungary, the Czech Republic, Slovakia and Romania are opposed to this, with the Czech prime minister reiterating his country's position on Sunday.
"I think it is impossible to retreat... Our position is firm," Bohuslav Sobotka said in a TV interview.
Meanwhile, Greece's coastguard says at least 28 people drowned when a boat carrying migrants capsized near the island of Farmakonisi on Sunday. Another 68 were rescued.
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.