A regional branch of Germany's far-right AfD party on Wednesday said it had made "a mistake" handing out a children's colouring book at a public event that contained denigrating caricatures of Muslims and black people.

Police in the western city of Krefeld said they were investigating a complaint of incitement to hatred filed against the Alternative for Germany's (AfD) parliamentary group in the state of North Rhine-Westphalia.

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The colouring book was handed out at an event organised by the parliamentary group in Krefeld on Monday.

Pages of the book spread quickly on social media, causing widespread outrage.

The drawings show men armed with guns waving Turkish flags, and headscarved women surrounded by children.

Another shows a swimming pool filled with fully covered women, and black people - with bones in their hair - harassing female bathers.

After initially defending the colouring book as "satire", the AfD's North Rhine-Westphalia parliamentary group issued an apology.

It had been "an organisational mistake" to print the book in its current form and hand it out, it said, adding that the project had been cancelled.

"Although the majority of the sketches remain within the scope of the project, there are some that are definitely not OK and, of course, do not reflect the opinions of the parliamentary group," it said.

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Founded in 2013, the anti-immigrant, anti-Islam AfD has shaken up Germany's political landscape and is now the biggest opposition party in the national parliament.

A speaker for the North Rhine-Westphalian parliament said they were investigating if the book was paid for with public funds.

A local politician from the centre-left Social Democratic Party (SPD), Thomas Kutschaty, tweeted that the AfD had "published a racist colouring book" that belonged in the bin.

Green Party youth member Jonas Stickelbroeck, who posted pictures of the colouring book on Twitter, told the Bento news website he was shocked by the stereotypes depicted.

He said the book exposed the AfD "for the racist party that it is".

Earlier this month, a regional president in Germany was forced to step down after receiving support from the AfD - breaking a long-standing pact between mainstream political parties to avoid working with the far right. The scandal in Thuringia, eastern Germany, also led the leader of the country's governing Christian Democrats party to announce she would not stand as a candidate to become chancellor when Angela Merkel steps down next year.