It disclosed this in a statement jointly signed by its Chairman, Niyi Akinsiju, and Secretary, Cassidy Madueke, on Thursday in Abuja.
It said latest information from the field showed that sustained air and land operations were yielding fruitful results in many places where they had been deployed.
It said that Zamfara and Borno were places where the military had been recording tremendous successes.
The army has in the last four weeks, been engaged in intense firefight with Boko Haram terrorists on several fronts, in Borno, even at a time the rest of the country had its attention fixed on the elections.
Reports from the theatre of the various operations show that the insurgents were beaten back as they attempted to infiltrate troops location around Bula-Yobe, Banki axis in Borno, it said.
The BMO said in the same week, soldiers of the Multinational Joint Task Force (MNJTF) killed no fewer than 50 terrorists and destroyed as many as 70 gun trucks.
Also troops deployed to stem the tide of banditry in Zamfara killed 55 bandits and rescued about 760 kidnapped victims within a two-week period.
About 24 people, including suspected informants and logistics suppliers for the bandits, were also arrested and handed over to the Police for possible investigations and prosecution.
But surprisingly, these success stories are not getting the type of traction. Mainstream and social media are known to regularly give negative stories or unverifiable Boko Haram propaganda, it said.
The BMO said an integral part of the successful military operation in the two states was the coordinated air surveillance missions which paved the way for a successful interdiction of the terrorists.
It is gratifying to see land and air troops coordinating quite well to the extent that series of day and night Intelligence, Surveillance and Reconnaissance (ISR) missions are conducted in the affected areas.
This was followed by air strikes on Boko Haram logistic facilities and fighters in several locations within three days, it said.
The group said in Zamfara, the air component of Operation Sharan Daji carried out air raids in Kagara, Gando, Fankama, Fete and Dumburum forests.
It said the air raids were to soften the ground for troops to rescue 760 abductees, consisting of men, women and children taken from various communities in the state.
It said that these sustained operations took place at a time the army deployed soldiers to assist the police on electoral duties in states prone to political violence.
This shows that the Nigerian military has the capacity and capabilities to deploy officers and men in volatile areas such as the Niger Delta.
At the same time, the Nigerian military has the capabilities to sustain its operations against terrorists on the fringes of the Lake Chad, and bandits in the forests of Zamfara, the BMO said.