Munich (Germany) (AFP) - Munich mayor Dieter Reiter vowed he would not give up in the face of the daunting challenge posed by a record influx of refugees, but made a plea on Sunday to give his city a chance to catch its breath.

"The night was long. We managed but we need a regulated, sustainable system to distribute the arriving refugees across Germany," he said, a day after 13,000 refugees poured into the southern German city.

"Every train that does not travel to Munich helps us," he said, adding quickly: "I am not easily depressed. I will not give up in any case."

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

Scenes of Germans waiting at Munich station, carrying "Refugees welcome" banners and clutching teddy bears to give to weary children after their long journey from war and persecution, have also become endearing images of the unprecedented migrant crisis hitting Europe.

"The generosity of the Munich people remains incredible," Colin Turner, a spokesman for volunteers at the Munich rail station, told AFP.

"Just five minutes after we launched our appeal yesterday on social networks for mattresses and sleeping bags, the first donations arrived.

"When I saw the amount of mattresses that the people brought and also all these people who came to help, I had tears in my eyes," he added.

- Passenger trains requisitioned -

Despite the generosity of the population, it was clear that the city's infrastructure to welcome the new arrivals was under severe strain.

Some 63,000 migrants arrived by rail at the main station since August 31, authorities said.

"Given the numbers from yesterday, it is very clear that we have reached the upper limit of our capacity," said a spokesman for Munich police.

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 dozen, 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.

One such train linking Munich to Berlin will be affected Sunday, with passengers told to rebook their trains.

The decision did not always prove popular with everyone, with a passenger with a first-class ticket seen making her objections very loudly at the counter.

"She made quite a scene," said the female employee at the counter.

Other regular services will be requisitioned on Monday, as the southern German city seeks to rapidly transport refugees onwards to other locations across the country in order to free up space for new arrivals.

Elsewhere in the station, some refugees were queuing at the reception centre, where they were to undergo medical checks before being sent on to shelters in the region or put on trains to other parts of Germany.

Most of the new arrivals are young men, and around them are volunteers wearing fluorescent vests, ever at the ready and who have been there distributing water and other provisions for hours.