Officials have slapped a round-the-clock curfew on a restive Nigerian state as security forces hunt for members of a radical Islamist group, the military said Sunday.

The ban on movements in the northeastern state of Yobe was imposed late Saturday, hours before a suicide bomber killed a woman and a child in attack outside a church in neighbouring Bauchi state.

No group has claimed the church blast, but it resembled previous attacks by Boko Haram, blamed for killing more than 1,400 people across northern and central Nigeria since 2010.

The group has repeatedly targetted Yobe, where state officials have ordered residents in two main cities to remain in their homes during an ongoing military operation aimed at cracking down on the Islamists.

"A 24-hour curfew has been imposed on Damaturu and Potiskum by the (Yobe) state government to clean up the state of terrorists," said Lieutenant Lazarus Eli, the military spokesman in Yobe.

"Residents of the two cities are to remain indoors until further notice to enable security personnel to fish out Boko Haram terrorists," he said.

After the curfew was announced, suspected Boko Haram gunmen battled security forces in a shootout in the Sabon Fegi area of Damaturu, one of the Islamist group's strongholds. Residents reported hearing explosions and gunshots in the area.

Eli said troops arrested 25 militants following the gun battle and recovered a large cache of weapons including Kalashnikovs and rocket-propelled grenades.

He denied residents' accusations that soldiers had committed abuses against civilians during the operation.

Rights groups have repeatedly accused Nigeria's military of using heavy-handed tactics in their campaigns against Boko Haram.

Damaturu was already under a dusk-to-dawn curfew, imposed following running gun battles between the military and suspected Islamists in June.