Explosive devices were used in some attacks, and in one incident townspeople rounded up gunmen and killed some of them, reports said.
Despite the violence, President Goodluck Jonathan said Sunday Nigeria was "still largely safe" and urged people to carry on with their daily activities, the Leadership newspaper reported Monday.
A security official said six people died Monday and several others were injured when hundreds of youths and security personnel rounded up gunmen suspected in the deaths of several of Azare's prominent citizens, the Daily Trust reported.
Members of the militant Boko Haram were suspected in the attack. Boko Haram, an Islamic extremist group, wants Sharia, legal code of Islam, for all of Nigeria, which has a large Christian population.
The incident followed the death of Alhaji Abbas Ibrahim Shehu, a member of the Katagum Emirate. who was killed Saturday in front of his residence in Azare.
Officials, speaking anonymously, said townspeople chased outsiders after hearing intermittent gunfire, and killed some of them..
On Sunday, suspected Boko Haram gunmen attacked a police station in Gamboru-Ngala, killing two officers and sending residents fleeing for safety, the Nigerian's Guardian newspaper reported.
A resident told The Guardian about 50 gunmen attacked the station with improvised explosive devices and Molotov cocktails, chanting "God is great" in Arabic.
Offices for immigration, customs and the State Security Service also were attacked, were several churches, a vaccination clinic and some communication towers, the Daily Trust said.
Two days earlier, a similar assault occurred in Damasak and several security officers died.
Gunmen attacked a town in Chibok Local Government Area in northeastern Nigeria Saturday, killing at least 10 people, including a local religious leader, and leaving many houses destroyed by fire, the Daily Trust said Monday.
In Yobe state, a joint task force discovered a bomb-making factory Sunday in Damaturu, considered a safe haven of the Islamic group, officials said. The discovery occurred during a search operation.
Jonathan, in a statement issued by his office, said insurgents worldwide attack to spread fear among citizens.
"Some dailies reported that nowhere is safe in Nigeria. In truth this ... is not correct. President Jonathan wishes to assure Nigerians that in spite of this situation, the country is still largely safe and secure," the statement said.