Nigeria's interior minister believes the fight against Boko Haram will be successful enough for the postponed elections to go ahead, he told the BBC.
Abbo Moro said he had been advised by the military that enough troops would be available in six weeks' time to secure the presidential ballot.
Officials say they delayed the vote to 28 March because troops needed for security are fighting the militants.
Opposition candidate Muhammadu Buhari has made a plea for calm.
But he said the independence of Nigeria's electoral commission had been "gravely compromised" by the decision to postpone the elections.
Meanwhile Boko Haram on Monday launched a third attack in four days on neighbouring Niger, targeting a prison in the border region of Diffa.
The militant group, which killed at least one person in a similar attack on Sunday, were reportedly pushed back after clashing with Nigerian forces.
Saturday's decision to postpone the presidential poll was welcomed by the ruling party of incumbent President Goodluck Jonathan though the US said it was "disappointed".
Parliamentary elections due to take place on 14 February have also been postponed to 28 March, and elections for state governors and assemblies slated for 28 February have been moved to 11 April.
Boko Haram attacks during election campaign
- 8 January: President Jonathan opens his election campaign
- 14 January: Nigerian military repel attack on the town of Biu in the north-eastern state of Borno
- 18 January: Suicide bomber kills four people after detonating a car bomb at a bus station in north-eastern Yobe state
- 25 January: Militants attack strategically important north-eastern city of Maiduguri, with dozens reported killed
- 4 February: Militants kill up to 70 people in attack on Cameroon
- 6-8 February: Attacks on Niger repulsed by Niger's military
'Free and fair'
Mr Moro said a regional coalition formed recently to fight Boko Haram was gaining the upper hand.
"I think that we don't have any reason not to be optimistic that they [the Nigerian military] are capable to bring the war to a level that will allow for a free and fair election," he said.
"I think that they know what stakes are involved - it's a national election, it's a national concern and the international community is watching."
Mr Buhari cautioned against any retaliatory acts of violence.
He said they could "only complicate the security challenges in the country".
A close race is being predicted between Mr Buhari, a former military ruler, Mr Jonathan.
Opposition officials accuse the military of forcing the electoral commission into the delay to help the sitting president's campaign.
The Boko Haram insurgency has led to more than a million people fleeing their homes, and the conflict is now poised to draw in neighbouring countries.
On Saturday Nigeria and the governments of Cameroon, Chad, Niger and Benin agreed to establish a force of 8,700 troops, police and civilians to fight the group.
Niger's parliament was due to vote on Monday on whether to contribute 700 of its troops to the force.
Abubakar Shekau, the leader of Boko Haram, vowed to defeat the regional force. In a video released online, Shekau said the coalition force was not large enough.
"By Allah, it is little. We will capture them one by one," he said.