Members of the far-right party Alternative for Germany (AfD) have backed an election manifesto that says Islam is not compatible with the constitution.
Delegates at the party's conference on Sunday also supported a call to ban minarets on mosques and the burqa.
Set up three years ago, the AfD has been buoyed by Europe's refugee crisis, which saw the arrival of more than one million people, mostly Muslims, in Germany last year.
The party has no MPs in the federal parliament in Berlin but has members in half of Germany's 16 regional state assemblies.
Opinion polls give AfD support of up to 14 percent, presenting a serious challenge to Chancellor Angela Merkel's conservatives and other established parties in the lead-up to the 2017 federal election.
Most mainstream parties have ruled out any coalition with the AfD.
In a noisy debate on the second day of a party congress, many of the 2,000 members cheered calls from the podium for measures against "Islamic symbols of power" and jeered at a plea for dialogue with Germany's Muslims.
"Islam is foreign to us and for that reason it cannot invoke the principle of religious freedom to the same degree as Christianity," said Hans-Thomas Tillschneider, an AfD politician from the state of Saxony-Anhalt, to loud applause.
|Anti-immigration parties which regard Islam as unwelcome in Germany have been buoyed by Europe's refugee crisis [Reuters]
Merkel has said that freedom of religion for all is guaranteed by Germany's constitution and has said on many occasions that Islam belongs to Germany.
Up to 2,000 left-wing demonstrators clashed with police on Saturday as they tried to break up the first full AfD conference.
About 500 people were briefly detained and 10 police officers received light injuries, a police spokesman said.
The chapter of the AfD manifesto concerning Muslims is entitled "Islam is not a part of Germany".
The manifesto demands a ban on minarets, the towers of a mosque from where the call to Muslim prayer is made, and the burqa, the all-encompassing body garment worn by some conservative Muslim women.
Germany is home to nearly four million Muslims, about five percent of the total population.
Many of the longer established Muslim community in Germany came from Turkey to find work, but those who have arrived over the past year have mostly been fleeing conflicts in Syria, Iraq and Afghanistan.
Last month the head of Germany's Central Council of Muslims compared the AfD's attitude towards his community with that of Adolf Hitler's Nazis towards the Jews.