BERLIN—Germany’s upstart Alternative for Germany party on Sunday adopted a clear anti-Islam stance in a platform that lays the foundation for the populist party’s bid to win parliamentary seats in federal elections next year.

The manifesto adopted by members gathered in Stuttgart for a party conference states that “Islam is not a part of Germany” and rejects minarets and the Muslim call to prayer—the clearest move yet by the party to harness widespread concern in Europe’s largest country about steeply rising refugee numbers...