"We estimate that since the beginning of the year, around 45,000 people who have entered [Germany] without permission haven't been processed by the identity service, even though this is laid out in the law on asylum applications," GdP deputy president Jörg Radek said.

The law requires authorities to take fingerprints of anyone caught crossing the border from Austria in to Bavaria – a common route for refugees from Africa. the Middle East and especially the Balkans arriving through southern Europe.

But Radek said that officers and their obsolete computers were massively overloaded in the Freyung and Passau areas of the Free State.

The Interior Ministry rejected the police complaints, with a spokesman saying that it was only at certain times of peak intensity that other authorities had to step in to help.

GdP believes that many refugees simply travel onward without allowing themselves to be registered, although between 250 and 300 people are stopped daily in Passau for identity and criminal record checks, with their details not stored on any database.

Police send them to the Federal Office for Migration and Refugees, but there's no check on whether they actually report there, Radek said.

Authorities running short of tents

Meanwhile, in Hamburg there were complaints that the whole country is running out of tents and containers in which to house refugees.

"In the whole country, there is extreme demand," Hamburg's interior senator Michael Neumann told the Hamburger Abendblatt on Monday.

Last week, the port city went ahead with setting up tents in an area where local people had protested fiercely against hosting any refugees, with a 3,000-capacity 'container village' planned for the future.

Authorities say that between 200 and 300 refugees arrive in Hamburg every day.

Berlin, Hamburg 'check refugees' genitals'

Hamburg and Berlin remain the only cities in Germany where doctors are asked to estimate refugees' ages based on examining their genitals and breasts.

A survey by dpa showed that all the other German states have put a stop to the practice.

States including Thuringia and Rhineland-Palatinate have declared the genital examinations to be insufficiently accurate.

"Even the best medical methods have a margin of error of two to three years," a spokesman for the Thuringian youth ministry said.

Hamburg's government says the purpose of the exams is to verify whether or not refugees are minors and that the tests are voluntary.

Authorities have different responsibilities towards minors than they do towards adult refugees under the law – with minors' more treatment being more expensive.

But the president of the city's medical council said that doctors were becoming the "extension of the state,“ and that saving money was no reason to put people through the exams.

Berlin's Charité hospital said that genital exams were not obligatory when forensically determining someone's age and that people were allowed to refuse the test.

Germany's other federal states rely on appearance and conversations with the young people to determine their age.