Munich is at the limit of its capacity to welcome refugees arriving en masse in Germany, police say, a day after 13,000 asylum-seekers reached the city.

“Given the numbers from yesterday, it is very clear that we have reached the upper limit of our capacity,” said a police spokesman on Sunday.

“Our aim today would be to transport as many as possible out of here, to make place for new arrivals,” he said.

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The police spokesman had earlier given a figure of 12,200 asylum-seekers arriving on Saturday, but government sources later said the actual number was 13,015.

Munich has become a key arrivals point for refugees travelling to Germany by train through Hungary and Austria.

Last weekend, about 20,000 migrants arrived at the city’s main railway station.

The president of the Upper Bavaria region, Christoph Hillenbrand, said he did not know “how we can cope”, according to the Bild am Sonntag tabloid which headlined its article “Munich at the brink of collapse”.

Bavarian public television BR said the city “came very close to a humanitarian disaster”, although authorities managed to limit the numbers of people sleeping on mattresses on the floor to just a few dozens, rather than the hundreds as earlier feared.

Authorities are mulling whether to open up the Olympiahalle – a stadium used for the 1972 Olympics and which today serves as a concert hall or sports arena – as a temporary shelter for the refugees.

In a sign that authorities were running out of options, regular passenger trains will be cleared out to transport refugees instead.

The army said it had mobilised some 600 soldiers on Saturday to help manage the migrant inflow.

Hungarian border fence nears completion

A four-metre-high barrier being built along Hungary’s 175km border with Serbia is aimed at stopping the several thousand migrants who enter Hungary – and therefore the EU – every night.

With 175,000 having crossed this year, it is one of a raft of measures – many of them highly controversial – announced by Hungary’s rightwing Prime Minister Viktor Orban in an effort to stem the flow.

But the fence is behind schedule.

Last month, Hungary completed the first stage of the barrier, piling up three coils of razorwire along the length of the frontier which has done little to halt the influx.

But the main part has yet to be finished.

Hungary’s parliament has also passed a raft of tough new laws that come into effect on Tuesday, meaning anyone crossing the border illegally can be deported or even jailed.

“From September 15, the rules are changing in Hungary, if you cross the border illegally, you will be immediately arrested by the authorities,” Orban said on Friday.

The UN refugee agency has warned that criminalising illegal border crossings could violate the UN Convention on Refugees if it involved asylum seekers.