German authorities warn that migrants seeking out Arabic-language mosques in search of the familiar are increasingly ending up at those attended by Islamist radicals. In interviews, security officials from Berlin to the southwest German state of Saarland said they have registered a sharp rise in the number of asylum-seekers attending mosques they believed attracted extremists.

Federal officials said they have counted more than 100 cases in which Islamists known to them have tried to establish contact with refugees. According to state and local agencies across the country, Islamists have offered migrants rides, food, shelter and translation help. In some cases, they have invited them to soccer games and grill parties, or brought them copies of the Quran and conservative Muslim clothing.

“They start by saying, ‘We will help you live your faith,’ ” said Torsten Voss, the head of the German domestic intelligence agency’s Hamburg branch. “The Islamist area comes later—that is, of course, their goal.”