There were cracks in the steeple, and the southeastern wall would somehow have to accommodate a niche pointing toward the holy city of Mecca, in Saudi Arabia, but those were not the biggest misgivings Daniel Abdin had about buying the Capernaum Church here in 2012.

More daunting than the millions of dollars in renovation costs was how residents of Horn, the working-class district where the church has stood since 1961, would react when they learned that Mr. Abdin and his thriving Muslim congregation planned to turn the derelict building into a mosque.

A church was "the last thing that we wanted," said Mr. Abdin, 52, the director of the Islamic Center Al Nour in Hamburg, during a recent interview outside the former Lutheran church, a squat modernist structure of concrete and red brick that construction workers were slowly encasing in scaffolding.

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