He acknowledged the militants were a ?real security threat? and said that close to 50% of Nigeria?s army was now deployed to the north-east.
Boko Haram took up arms in 2009.
It says it is fighting to create an Islamic state.
Since the government declared a state of emergency 20 months ago in three north-eastern states to deal with the insurgency, the group has strengthened and now controls several towns, where it has declared a caliphate.
The militants gained worldwide notoriety after kidnapping more than 200 schoolgirls in April last year ? who have yet to be rescued.
Recently they have carried out raids into neighbouring Cameroon and this week Boko Haram?s leader said his fighters had carried out the brutal attacks on the Nigerian town of Baga.
He said they had seized enough weapons from Baga?s military base to ?annihilate Nigeria?.
Some reports said that as many as 2,000 people died in Baga but Nigeria?s government has disputed this, putting the toll at 150.
Mr Dasuki told the BBC?s Newsday programme the fact that so many of the country?s security sources had been deployed to deal with the militants showed how seriously the situation was being taken.
When asked if Nigeria needed outside help, he said ?No?, before saying it was an option to involve UN and AU forces, but regional partners were best placed to deal with the problem,
Nigerian soldiers currently make up the bulk of UN peacekeepers deployed to Africa, the security chief has said.
On Thursday, he criticised ?cowards? within the armed forces for hampering the campaign against the insurgents.