Police in Cologne say the number of criminal cases relating to violent attacks in the city on New Year’s Eve has risen above 500.

The German justice minister, Heiko Maas, said the authorities needed to work quickly to establish whether Cologne's violence was linked to incidents reported in other cities.

The chief of police in Cologne has been sacked in the wake of the scandal, after up to 1,000 men were allowed to mug, accost and sexually abuse women in "coordinated" attacks in a city square.

Women march through Cologne holding placards reading ‘Against Sexism, Against Racism’ (Reuters)

Police said on Sunday that of the 516 criminal complaints made since the violence 10 days ago, around 40 per cent involved allegations of sexual offences.

Initial reports had suggested scores of women were targeted, while just 31 suspects have been detained by police for questioning, 18 of whom were asylum seekers.

Speaking to Bild, Mr Maas said: "If such a horde gathers in order to commit crimes, that appears in some form to be planned. Nobody can tell me that this was not coordinated or prepared."

On Saturday, the German chancellor Angela Merkel announced a proposal that will make it easier for the authorities to deport refugees and migrants who commit crimes.