“For me, it is self-evident that the Muslims need to have a prestigious place of worship,” said Mr. Schramma, who belongs to the center-right Christian Democratic Union. “But it bothers me when people have lived here for 35 years and they don’t speak a single word of German.”

Cologne’s Roman Catholic leader, Cardinal Joachim Meisner, is similarly ambivalent. Asked in a radio interview if he was afraid of the mosque, he said, “I don’t want to say I’m afraid, but I have an uneasy feeling.”

These statements rankle German-Turkish leaders, who have been working with the city since 2001 to build a mosque on the site of a converted drug factory, which now houses a far smaller mosque, a community center and the offices of the Turkish-Islamic Union for Religious Affairs.

“The 120,000 Muslims of Cologne don’t have a single place they can point to with pride as the symbol of our faith,” said Bekir Alboga, leader of interreligious dialogue at the union, which is known as Ditib. “Christians have their churches, Jews have their synagogues.”

Mr. Alboga, a 44-year-old Turkish imam who immigrated here at 18 and speaks rapid-fire German, said the mosque would be a “crowning moment for religious tolerance.” Given Germany’s dark history, he added, “German politicians need to be careful about what they say.”

Mr. Alboga said he was particularly dismayed by Cardinal Meisner, because the Catholic Church, along with Germany’s Protestant churches, has long supported the mosque. Ditib, he said, is a moderate organization that acts as a “bulwark against radicalism and terrorism.” It plans to finance the project, which will cost more than $20 million, entirely through donations.

Image Bekir Alboga, top, an imam, with a model of the mosque, which he supports. Manfred Rouhs, center, opposes it as a sign of a parallel Muslim society and Ralph Giordano, a writer, sees it as creeping Islamization. Credit... Marcus Gloger for The New York Times

The group must obtain a building permit before it can break ground, but Mr. Alboga said he was confident the mosque would not be blocked. Ditib has agreed to various stipulations, including a ban on broadcasting the call to prayer over loudspeakers outside the building.