Two members of the Tableeghi Jamaat died on the spot, while four people were seriously hurt and taken to hospital, he said.
Authorities had detained some 15 Afghan refugee suspects in the area as part of their investigation into the attack.
Kurram, a usually-quiet tribal district, borders Afghanistan and the rugged North Waziristan tribal zone, where troops are hunting al Qaeda linked militants and where Taleban forces killed 17 in a clash on Sunday.
Taleban attacks in the Afghan south-east have surged in recent months ahead of Afghanistan's landmark parliamentary elections in September.