BERLIN (Reuters) - The anti-immigration Alternative for Germany (AfD) broke off talks on Monday with representatives of the Muslim community that had been intended to ease tensions after the party declared Islam incompatible with the German constitution.

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

Last month Aiman Mazyek, leader of the Central Council of Muslims that organized Monday’s talks, likened the AfD’s stance towards Muslims to that of the Nazis toward Jews in the 1930s after Perry’s party called for a ban on minarets and burqas.

“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 “Comparisons made time and again that the AfD is becoming more like the Third Reich were not withdrawn.”

German Muslims have been alarmed by the rise of the AfD, which entered three state parliaments in March by attracting voters angry with Chancellor Angela Merkel’s welcoming of refugees fleeing conflicts in Syria, Iraq and elsewhere.

The influx of more than one million mostly Muslim migrants into Germany last year has hardened German public opinion on immigration and pushed the government to toughen asylum rules.

This month AfD members backed an election manifesto that says Islam is not compatible with the constitution.

After Monday’s meeting Mazyek again criticized the AfD move.

“Above all, the saying ‘Islam doesn’t belong in Germany’ makes it clear that populism, defamation and the promotion of prejudice persist,” he said.

Some four million Muslims live in Germany, making up almost 5 percent of the total population.

AfD wants drastically to reduce the number of refugees in Germany by rejecting Syrians and Iraqis who come from “safe third states” such as Turkey and Lebanon and turning down asylum applicants without identification documents, among other steps.

It also wants to cut to 48 hours the processing time for asylum applications.