"The capture of a number of terrorists believed to be the ringleaders of those operating around Alagarmo sparked off a major fight on the outskirts of Bulanbuli, Borno State last night," defence spokesman Major General Chris Olukolade said in a statement.
"Over 40 terrorists died in the encounter while 4 soldiers lost their lives and 9 were wounded," he said in the statement e-mailed to AFP.
Bulanbuli is between Alagarmo and Sambisa forest where the students, who were abducted early last week, are believed to be held.
The April 14 kidnapping came hours after the deadliest attack yet in Nigeria's capital -- a bomb blast at a crowded bus station that killed at least 75 people.
Boko Haram leader Abubakar Shekau claimed responsibility for that attack.
Residents in Chibok said a series of explosions overnight yesterday rocked an area where the more than 200 school girls are being held.
The safe release of the school girls topped the agenda of a meeting Nigerian President Goodluck Jonathan held Thursday with political and military chiefs, a governor had said.
But it is not clear if the latest clash with the insurgents was part of new security measures taken after that meeting.
"For most of the night we kept hearing huge explosions from afar coming from Sambisa forest. There were 30 explosions in all," a resident, Haladu Sule told AFP.
"We believe the explosions were from deep inside Sambisa forest where our girls are being held by Boko Haram but we don't know if it is a rescue operation by soldiers to free the girls," said Enoch Mark, whose daughter and two nieces were among the kidnapped girls.
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