The dead included the spokesperson for the sect known as Boko Haram, as well as a commander who operates in Kogi state south of Nigeria's capital, the official said.
The killings could prove to be a boon to Nigeria's security forces, which remain largely unable to stop guerrilla attacks and bombings by the sect, which killed another 13 people this weekend alone, authorities said.
The shooting occurred on Monday morning in Mariri, a town to the southeast of Kano, the largest city in Nigeria's Muslim north. There, soldiers stopped a vehicle with the sect spokesperson, the commander, the spokesperson's wife and their children, the official said.
It is unclear what happened next, though the official said soldiers shot dead both the commander and the spokesperson. The wife and children remain in military custody, the official said.
The wife told soldiers the men had accompanied her to Kano where she sought medical help, the official said.
The official spoke on condition of anonymity as the information was not to be made immediately public Monday. Lieutenant Iweha Ikedichi, a military spokesperson in the region, later told journalists that soldiers had only killed one man, the Boko Haram spokesperson.
The official who spoke to the Associated Press had been at the checkpoint and offered further details about the scene.
Government officials may be hesitating as they previously claimed in February to have arrested the sect's spokesperson, who uses the nom de guerre Abul Qaqa when speaking to journalists.
Only days afterward, a spokesperson using the same name told journalists: "We are waxing stronger by the day despite the arrest of some of our top members." The sect also threatened journalists who previously reported on the government's claim without mentioning Boko Haram's denial.
Also on Monday, a Nigerian army soldier and 13 suspected Boko Haram members were killed in the northeastern city of Maiduguri. An explosive was thrown at a military vehicle, killing one soldier and injuring three others, said a security source who spoke on condition of anonymity. A shootout then occurred in which the 13 suspected Boko Haram members were killed.
The sect, whose name means "Western education is sacrilege" in the Hausa language of Nigeria's north, has been waging an increasingly bloody fight against the nation's government.
More than 680 people have died in drive-by killings and bombings blamed on Boko Haram this year alone, according to a count by the Associated Press. The sect has demanded the release of all its captive members and has called for strict Sharia law to be implemented across the entire country.
The killing of members of the sect's senior leadership comes as the group recently changed some of its tactics and attacked more than 30 mobile phone towers throughout northern Nigeria, disrupting communications in a nation reliant on cellular phones.
Abubakar Shekau – the leader of the sect who occasionally appears in videos posted to the internet – remains at large. Security officials and experts believe he and other Boko Haram members are hiding somewhere in the neighbouring countries of Cameroon, Chad or Niger.
The US in June placed financial sanctions on Shekau and two other high-ranking Boko Haram members, though it remains unclear whether the group has any assets in America or use banks there.
American officials also have said Boko Haram has loose ties with al-Qaeda in the Islamic Maghreb and the Somali terrorist organisation al-Shabab.
The group's attacks also raised ethnic and religious tensions in Nigeria, a nation of more than 160-million people largely split between a Christian south and a Muslim north.
This weekend, killings blamed on Boko Haram continued.
In Kano, police said a security agent and three of his family members were shot dead on Sunday by sect members. Gunmen attacked a suburb on Sunday on the outskirts of Bauchi, killing eight people who were playing poker, state police commissioner Muhammad Ladan said.
Assailants also shot dead a respected moderate Muslim cleric in Maiduguri, the northeastern city that's the sect's spiritual home, authorities said. – Sapa-AP