BEIRUT—At least 50 Syrian security-force members were killed in a suicide car bombing claimed by an extremist group on Monday, as opposition figures met in Qatar in a U.S.-backed effort to unite rebel groups and stem the rising influence of such extremists.

The attack, on an outpost near the central city of Hama, came amid strikes that killed dozens more people, including the bombing of a regime enclave of the capital, Damascus, and government attacks on rebels around the city and elsewhere.

On...