Boko Haram said it carried out a series of bombings in Kano last Friday in which at least 185 people died.
The organization says it wants to overthrow the Nigerian government and impose Islamic law.
There were two casualties from Tuesday’s dawn raids, carried out by the Nigerian Joint Military Task Force.
One resident of Kano said officers had encircled a house where a Boko Haram suspect was believed to be hiding. The shoot-out lasted several hours.
“They began shooting, and he fired back… This was followed by a barrage of gunfire by the security men,” Mohammed Maikubi Bala told AFP news agency.
A man and his wife were killed in the raid, residents said.
In a statement released on Tuesday, Amnesty said the Nigerian government should do more to tackle the group.
“The Nigerian government has repeatedly failed to prevent, investigate, prosecute or punish these acts,” it said.
The key suspect in a Christmas Day bombing on a Catholic church – believed to be a member of the Islamist sect Boko Haram – escaped from police custody earlier this month.
At least 40 people died in that attack.
A top African Union official warned that the radical sect was escalating its activities.
“The possibility of this group expanding its activities into the neighboring countries, deep into the Central African region should not be discarded,” said Francisco Caetano Jose Madeira, in charge of counter terrorism co-operation for the AU.
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