He is the most senior security official to be killed by Boko Haram so far.
It does not offer much hope for dealing comprehensively with the underlying causes of the Boko Haram phenomenon.
Among those targeted by the military was the Islamist militant group Boko Haram.
No-one has admitted the abductions but the Islamist militant group, Boko Haram, has staged a series of attacks in northern Nigeria.
BBC: Nigeria foreign workers abducted in Bauchi state - police
On Thursday, France confirmed it had "received information that the group Boko Haram is claiming to be holding the French family".
President Jonathan made the announcement after reportedly holding talks with religious and political leaders from the country's north, considered Boko Haram's stronghold.
The ambush came after 55 people were reportedly killed in the north-east of Nigeria in co-ordinated attacks by the Boko Haram Islamist militant group.
But Brig Gen Edokpaye disputed this, saying Boko Haram's weapons had exploded, causing "fire to about 30 thatched houses in the predominantly fishing community".
Since late 2011, Potiskum, about 500 kilometers (300 miles) northeast of Nigeria's central capital, Abuja, has been targeted by Boko Haram fighters in attacks.
Western diplomats tell CNN that Nigeria, for example, is more concerned about the threat from Boko Haram within than jihadist safe havens in Mali.
CNN: Algeria attack changes terror landscape in North Africa
Some analysts and Administration officials have claimed that the Afghan Taliban and Boko Haram, which fights for an Islamist Nigeria, don't coordinate with al Qaeda.
But analysts say those tactics are no different from the steps Nigerian officials have consistently used during the country's now nine-year conflict with Boko Haram.
Campbell also noted that while Ansaru has been quick to claim responsibility for its previous actions, Boko Haram had been largely silent in recent months.
Nigerian President Goodluck Jonathan has set up a panel to look into the possibility of granting an amnesty to the Islamist militant group Boko Haram.
Seven French nationals are still being held after they were kidnapped across the border in Cameroon by gunmen believed to be members of Boko Haram.
No-one has said they were behind the attack, but it happened in an area where the Islamist militant group, Boko Haram, has been active in recent years.
He has been accused of failing to "sell" his recent decision to cut fuel subsidies to the Nigerian public (and of "overselling" the threat posed by Boko Haram).
Nigerian troops say they have killed 14 suspected members of the Islamist rebel group Boko Haram, in a raid on a building in the northern city of Kano.
Some analysts believe it split from Boko Haram, because it was opposed to the increasing number of Nigerian civilians - both Muslims and Christians - killed in bombings.
No group has yet claimed responsibility for that attack either, though it follows alleged Boko Haram attacks now focusing on softer targets, like lightly guarded mobile phone towers.
The assault marks a significant escalation in the long-running insurgency Nigeria faces in its predominantly Muslim north, with Boko Haram extremists mounting a coordinated assault on soldiers using military-grade weaponry.
U.S. officials say Ansaru is an offshoot of the Islamist militant group Boko Haram, which Nigerian authorities say is behind a recent rash of killings and kidnappings in the country.
Kano Governor Musa Rabiu Kwankwaso disputes the idea that banning the bikes is only going to deepen poverty and drive recruits into the hands of criminal groups, including Boko Haram.
Nigerian President Goodluck Jonathan says his government cannot grant an amnesty to the militant Islamist group Boko Haram because it is not known who its members are or what they want.
Nigerian troops killed at least 30 people when they opened fire and burned buildings in the north-eastern city of Maiduguri, which has been under attack by a militant Islamist group, Boko Haram.
Following the abduction, the French government said it believed the couple, their children aged five, eight, 10 and 12, and an uncle were taken across the border into Nigeria, probably by Boko Haram.
Last week, southern neighbor Nigeria said it was shutting much of its border with Niger and sending thousands of troops into the border areas in pursuit of a an Islamic insurgency called Boko Haram.
Elsewhere on the continent, I expect turbulence to continue in the eastern part of the Democratic Republic of Congo and sadly much against all hope I suspect Boko Haram attacks in Nigeria to continue.
The military statement said Mr Zangina was leader of Boko Haram in the "North Central part of Nigeria and co-ordinator of most of the suicide attacks and bombings in Abuja, Kaduna, Kano, Jos and Potiskum".
French officials immediately pointed the finger at the Nigerian group Boko Haram, which has waged a three-year terror campaign against Christians in northern Nigeria as well as attacking police stations and more moderate Muslims in authority.
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