The army captured the Sambisa Forest in the country's east over the weekend.
Speaking to Al Jazeera on Tuesday, Brigadier General Victor Ezugwu, the army commander, said that while his soldiers had made significant gains, they had not been able to track down the missing girls who were captured by Boko Haram in April 2014.
About 200 of the 276 Chibok girls who were taken remain missing. Some were believed to be in the Sambisa Forest.
"We are still searching for our dear daughters," Ezugwu said. "As I speak to you now, we've not been able to make contact with them because the insurgents are running away with the girls. We are still trailing them."
He added that "so far, we have rescued over 1,900 Nigerian citizens [from captivity]".
He said the operation against Boko Haram is ongoing.
"It's not finished business. It's a work in progress. At the end of the day it's a bright light at the end of the tunnel," he said.
While Nigerian authorities say they are working hard to find the missing girls, there are concerns over how those who have been freed are treated.
Kidnapped girls freed from more than two years of captivity were prevented by Nigerian officials from spending Christmas at home with their families and relatives, a lawyer said on Tuesday.
Parents said they were taken to see their daughters, but the girls who were not allowed to go home or go to a church service.
The news raised questions about Nigeria's handling of the 21 girls freed in October by negotiation with the group.
'Final defeat'
Boko Haram's insurgency began in Maiduguri, though it has since spread beyond Nigeria's borders to Chad, Cameroon and Niger.
Nearly 15,000 civilians have been killed since 1999, when Boko Haram launched a campaign to establish an Islamic state.
"We are on top of the situation, all hands are still on deck," Ezugwu said. "This defeat is final and it [Boko Haram] will not spread to other parts of West Africa."
His comments echoed those of Nigerian President Muhammadu Buhari, who on Saturday announced the "final crushing of Boko Haram terrorists" in a message posted to his Twitter feed.
Army officials told Al Jazeera that it took around 40 minutes to breach Boko Haram defences in Sambisa Forest.
"Now the biggest task of retaking Sambisa is over, the problem is how to secure the location," said Al Jazeera's Ahmed Idris, who is embedded with the army in Sambisa. "This whole area is booby trapped and mined."
Elsewhere, 31 Boko Haram fighters surrendered to authorities in Niger's southeast region, the West African country's Interior Minister Bazoum Mohamed announced on Tuesday.
Boko Haram has been carrying out attacks in Niger since February 2015.
"They came one by one and are currently held in a secure centre," a security source based in Diffa told the AFP news agency, adding that they would return to their families after undergoing a "de-radicalisation" programme.
