The far-right Alternative for Germany (AfD) leader has walked out of talks with the country's Central Council of Muslims.

The meeting on Monday was intended to ease tensions after the anti-immigrant party declared Islam incompatible with the German constitution.

AfD leader Frauke Perry said she walked out of the meeting after a prominent German Muslim refused to retract a comment comparing the AfD with Adolf Hitler's Third Reich.

"We had to let ourselves – and this really gets to us – be accused of being like a party out of the Third Reich," Petry told reporters. "Comparisons made time and again that the AfD is becoming more like the Third Reich were not withdrawn."

The meeting was coordinated by Aiman Mazyek, the leader of the Central Council of Muslims. Last month he likened the AfD's stance towards Muslims to that of the Nazis towards Jews in the 1930s, after the AfD called for a ban on minarets and burqas.

After the meeting Mazyek said the AfD had not wanted to discuss its anti-Islam policy and wanted to dictate how the Muslim council should slaughter animals and build mosques. He said the party would continue to "follow the path of populism, defamation and prejudice".

There has been a sharp rise in right-wing sentiment in Germany since Chancellor Angela Merkel adopted an open-door policy towards migration, allowing more than one million refugees and migrants into the country. The policy has hardened German attitudes towards migration and Merkel has since adopted a tougher approach.

Figures released yesterday showed there has been an increase in crimes related to extremist right-wing activity in Germany. In 2015 there were 23,000 attacks, according to the BBC, a 35 per cent increase on the year before.