A police official says gunmen believed to be members of an extremist group have shot dead a pastor in Kenya's coastal town, Mombasa.

Henry Ondiek, who is in charge of criminal investigations at the coast, said Sunday the pastor was shot at the entrance of the Mvita Primary School which hosts the Maximum Revival Centre, a mosque and another church and is guarded by police.

Ondiek did not say who was responsible for the attack, but it falls into a pattern of gun and explosive attacks at the Kenyan coast blamed on the al-Qaida-linked al-shabab militant group from Somalia.

Al-Shabab has vowed retribution for the presence of Kenyan troops fighting the militant group in Somalia. Kenya has suffered string of attacks since it deployed troops to Somalia in Oct 2011.