“It is appropriate to bring in classes on Islam in state schools or schools overseen by the state,” Gerd Landsberg, head of the association of local councils, told the Rheinische Post on Wednesday.
In this way the state can gain more control over the upbringing of Muslim youths, Landsberg said.
On Monday evening, an attacker whom investigators believe was a 17-year-old refugee from Afghanistan, seriously wounded four people with an axe and is reported to have shouted "Allahu Akbar" (God is great) several times.
Terror group Isis later released a video in which the youth made threats in Pashto while holding a knife.
Senior figures in the church had already called at the end of May for Islam classes to become compulsory at schools.
The head of the Evangelical Church in Germany (EKD), Heinrich Bedford-Strohm, said that religious education was the best way to immunize Muslim youths against the dangers of Islamist fundamentalism.
He also said he was in favour of Muslim religious associations taking over responsibility for providing this education, just as churches are responsible for religious education about Christianity.
Six of Germany's 16 states currently offer classes in Islam at school.