Senior German conservative politician Andreas Scheuer has said German must become the language of the country’s mosques and that foreign funding from Turkey and Saudi Arabia must stop.
The general secretary of the CSU, sister party of Chancellor Angela Merkel’s CDU, said political Islam was undermining integration.
His remarks came amid a German freedom-of-speech row involving Turkey.
The Turkish president has filed a legal complaint against a German satirist.
President Recep Tayyip Erdogan was angered by an obscene poem read out by Jan Boehmermann on public broadcaster ZDF.
The comedian explained that what he was saying broke German laws on free speech before going on to accuse the Turkish leader of having sex with goats and sheep.
His poem was broadcast days after the Turkish government complained to the German ambassador to Ankara about a satirical song on another German channel which mocked Mr Erdogan’s authoritarian style of government.
German prosecutors are currently considering whether Boehmermann should be charged with insulting a foreign leader in his obscene poem.
The satirist has been given police protection and this week’s broadcast of his programme has been halted.
The case has created a dilemma for Chancellor Merkel who, along with other European leaders, needs the Turkish government to fulfil its side of a deal to take back migrants who have crossed to the Greek islands.
European Commission President Jean-Claude Juncker stressed on Wednesday that Europe’s values on press freedom would not change, regardless of the importance of the refugee agreement. He did not make any specific reference to Boehmermann.
The German lawyer acting on behalf of President Erdogan said on Tuesday night that his client wanted Boehmermann to be punished “to get him back on the right path”.
In his interview with German daily Die Welt, Mr Scheuer said Mr Erdogan’s response was “hard to bear” and that Europe should not abandon its enlightened principles.
Asked about Turkey’s role in funding German mosques, he called for an Islam law that prevented foreign and sometimes extreme values from being imported from abroad.
“Financing of mosques or Islamic kindergartens from abroad, such as from Turkey or Saudi Arabia, must be stopped,” he said. “All imams have to be trained in Germany and must share our values. German must become the language of the mosque.”
Some three million people in Germany have at least one parent from Turkey and most mosques in Germany are part of the Turkish-Islamic Union for Religious Affairs (DITIB), a branch of the main Turkish religious authority.
While many of Germany’s imams do come from Turkey and are seen as officials of the Turkish state, several German universities have set up Islamic centres in recent years with the aim of training a new generation. Several Muslim communities have also moved to free themselves of influence from Ankara.