Lai Mohammed maintained the Nigerian government had greatly reduced the group's capacity to attack and was on its last week.
"Boko Haram has been largely defeated. They (Boko Haram) know they are on their way out," Mohammed told journalists in Lagos.
"They lack the capacity to launch horrendous attacks they used to do in the past. We have succeeded in dislodging them," he said.
"Our problem now is how to resettle the internally displaced people."
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In an expected show of defiance, Boko Haram attacked a series of towns in the north of Africa's most populous nation and biggest oil producer, calling into question Buhari's claim that the militants weren't capable of "conventional" attacks.
On Sunday evening, there was a spate of suicide bombings in the key city of Maiduguri, killing 21 people and injuring scores of others.
In the neighbouring state of Adamawa, 30 people were killed yesterday morning after two young women detonated explosives in a crowded market.
According to the Global Terrorism Index, a report released by the New York-based Institute for Economics and Peace, Boko Haram "has become the most deadly terrorist group in the world".
While Nigeria's military has won back swathes of territory from the jihadists in recent months, Boko Haram has expanded its network in neighbouring Chad, Cameroon and Niger.
The group has increasingly relied on children as weapons, often deploying young girls strapped with explosives into crowded marketplaces and mosques.