They said Muslims were being made to feel that "they carry partial blame because, after their mosques have been desecrated by neo-Nazis using pig heads and graffiti of crosses, they are now also being attacked by foreign terrorist groups".
"For decades, Muslims have faced a constant right-wing extremist threat" in Germany, said a joint statement by the Islamic Council, Central Council of Muslims, and the Coordinating Council of Muslims in Germany (KRM).
"This threat has been exacerbated by foreign terrorist groups."
This year had seen 27 attacks on Islamic houses of worship so far, ranging from graffiti to arson attacks, after more than 100 cases last year, said KRM spokesman Zekeriya Altug.
The detection rate for these offences is very low, said Islamic Council chairman Burhan Kesici at a joint press conference.