The groups want to ensure that Islam can be taught in German in public schools to better integrate children and prevent misinterpretations.
It is vital to resolve this problem and ensure that Islam is enrolled in school curriculums, said Nadeem Elyas, president of the central council of Muslims, one of the groups.
"If we don't, the next generation of Muslims will grow up without values, and if they don't get their religious education in schools they risk being influenced by bad interpretations of the Quran," he said after a meeting of Muslim groups in Hamburg last weekend.
Muslim groups in Germany define themselves by the number of mosques under their jurisdiction rather than by the number of people who are signed-up members, while the law only takes membership into account.
Though religious courses for the estimated 600,000 Muslim children living in Germany are guaranteed under the law, the Quran has not been accepted in the classroom.
As education in Germany is controlled by the 16 states, the group plans to create a unified and democratic structure at federal and state levels.
The project was snubbed by other major groups in Germany, stating that Muslims in some states had been trying to mount initiatives of their own but without great success.
Germany has been working on improving the integration of its Muslim community.
Chancellor Gerhard Schroeder has been increasingly keen to improve the integration of his country's Muslims, particularly with Turkey preparing to start talks to join the European Union.
Two Egyptian imams were banned from the country last month under new legislation which authorities say is aimed at "hate preachers" suspected of trying to spread "extremist" ideologies.