Germany's public prosecutor is to take action following a demonstration organized by Islamists with more than 1,000 participants in Hamburg at the weekend.
The individual slogans and banners will be examined for criminal offences, police chief Falk Schnabel told public broadcaster ZDF on Monday.
"However, it is also a fact that our Basic Law also allows extremist demonstrations with regard to freedom of assembly and freedom of opinion," he added.
The right of assembly is structured in such a way that it is not primarily about allowing or banning certain opinions, he said. "We are the police, our law is neutral."
The right of assembly is essentially about whether an assembly is peaceful, he said.
The rally, which took place in Hamburg on Saturday, passed off peacefully, but allegations of anti-Islamic policies and an anti-Islam media campaign in Germany were heard.
Some carried posters that read "The caliphate is the solution" or "Germany - a dictatorship of values."
According to the Hamburg authorities, the people registering the demonstration in advance, as required under German law, are close to the Muslim Interaktiv group, which has been classified by the intelligence services as extremist.