"After a mop up of scenes of battle (since Saturday), 14 terrorists were confirmed dead... Altogether three soldiers died, while seven are wounded and are being treated in a military medical facility," the defence ministry said in a statement.
Maiduguri has been the enclave of radical Islamist Boko Haram sect which has vowed to carve out an Islamic caliphate in the oil rich African country.
Meanwhile, airstrikes against the militants continued especially in areas distant from the state capital which the extremists have made their stronghold, subjecting locals to Sharia-type administration.
Supply routes to the militants were sealed and reinforcement sent to border posts to stop them from escaping, the military said.
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President Goodluck Jonathan had pronounced an emergency rule in the area last week.
Local TV channels quoted military spokesman Brig General Christopher Olukolade as saying that 14 insurgents were killed while scores were arrested in Maiduguri.
He also said that vehicles and weapons were recovered from them.
"Troops have continued the advance and attack on identified terrorist camps in the Northern part of the country. Patrols are also ongoing to secure towns and villages from infiltration, while curfews on identified flash points are being enforced," he said.
Boko Haram insurgents have been attacking government structures, killing politicians, government officials, traditional rulers, soldiers, police and civilians since 2009.
More than 2000 persons have been killed in their assaults.
Earlier, an amnesty committee was inaugurated by the country's president in a bid to seek truce but the group rejected the offer in a video message.