Militants from the fundamentalist Islamic sect, Boko Haram, carried out an attack in Maiha local government area of Adamawa state on Friday, killing 20 people.
In the second incident, unknown gunmen invaded Musari area of Borno State in the wee hours of the morning and killed five people.
The Adamawa attack saw the terrorists invading offices and lodges of the Customs and private residents.
They set ablaze a divisional police headquarters and set free 35 inmates after Maiha prisons was attacked.
Police spokesman in Adamawa state, Mohammed Ibrahim, has confirmed the attacks.
"The attackers went away with various arms and ammunition from the police headquarters," he said.
The military spokesman in Borno state, Lt Col Sagir Musa, has also confirmed the attack in his state.
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"Some terrorists sneaked into Musari, a village located on the outskirts of Maiduguri, and carried out the selective killings of five people including a serving Nigerian Police Traffic Warden," he said.
Radical sect Boko Haram wants to install an Islamic government in northern Nigeria where Muslims outnumbers Christians.
To forestall their ambition, the government of the oil-rich African country has set up a military Joint Task Force that battles them on a day-to-day basis.
They have killed thousands of people through suicide attacks, bombings and drive-by shootings since 2009.