In the North-central, Mr Buba said, the troops of Operation Safe Haven conducted several offensive operations.
The Defence Headquarters has said that troops killed no fewer than 640 terrorists, apprehended 1,051 suspects and rescued 563 kidnapped hostages in May.
The Director of Defence Media Operations, Edward Buba, disclosed this while briefing journalists on the operations of the Nigerian military on Thursday in Abuja.
He said that some senior terrorist commanders and fighters have been killed which has degraded the potency of the terrorists, as a result of intense pressure from the troops across theatres of operations.
Mr Buba, a major general, further said that the troops apprehended some suspects including their logistic suppliers and informants.
He added that the troops also recovered 707 assorted weapons, 16,487 assorted ammunitions comprising 411 AK47 rifles, 234 locally fabricated guns and 43 pump action guns, amongst others.
In the North-east, Mr Buba said, Operation Hadin Kai recorded huge operational successes by killing some key terrorists including one Malam Mohammed, a leader of the IED cell in Sambisa Forest.
He said the troops also rescued 386 hostages, who had been in captivity for over 10 years, adding that the victims had been handed over to the Borno State Government.
"During the month, troops neutralised 306 terrorists, arrested 199 suspects and rescued additional 219 kidnapped hostages.
"Troops also recorded 1,099 surrendered BH/ISWAP terrorists' combatants and their families as they recovered 200 AK47 rifles and 53 fabricated rifles among others," he said.
In the North-central, Mr Buba said, the troops of Operation Safe Haven conducted several offensive operations leading to the killing of 39 terrorists, while 140 suspects were apprehended with 77 hostages rescued.
"The troops also recovered nine AK47 rifles among others," he said.
According to him, troops of Operation Whirl Stroke have conducted several operations against terrorists and violent extremist strongholds and arrested violent extremists, their collaborators and several gunrunners.
Mr Buba also said the troops had killed 41 terrorists, arrested 184 suspects and rescued 48 kidnapped hostages as well as recovered 18 AK47 rifles, and 27 assorted arms, with 2,237 rounds of 7.62mm special.
In the North-west, Mr Buba disclosed, activities of the troops of Operation Hadarin Daji, led to the elimination of a notorious terrorist commander, Usman Modi.
"The troops killed the terrorist commander who hitherto terrorised communities around Danmusa, Kankara and Safana LGAs of Katsina State.
"Overall, the troops neutralised 262 terrorists, arrested 204 suspects and rescued 243 kidnap hostages," Mr Buba said.
He further explained that the air component of Operation HADARIN DAJI has recorded significant air strikes to destroy terrorist camps in Faskari, Bayan Ruwa Maradun and Anka Local Government Area of Zamfara.
"Some of the terrorist leaders targeted (were) Jammo Smally and Kachalla Halilu; additionally, terrorist enclaves at Tungar Daji in Zamfara State and Rugu Forest in Safana (LGA) were also engaged," he said.
The director said under Operation Whirl Punch, the troops neutralised 56 terrorists, arrested 150 suspects and rescued 80 kidnapped hostages as well as recovered 23 AK47 rifles.
According to him, the air component destroyed terrorists training camp in Kuduru, Giwa Local Government Area of Kaduna State and enclaves at Kabago, Alawa Forest, Katarma and Kwaki general areas in Shiroro and Chikun Local Government Areas of Niger and Kaduna states.
Other successful operations recorded by the army troops include Operations Delta Safe in the South-South, where troops prevented the stealing of 4.12 million litres of crude oil, 793,796 litres of AGO and 4,480 litres of PMS.
"The troops also recovered 73 assorted weapons, destroyed 129 wooden boats, 686 assorted ammunitions and 223 illegal refining sites as well as neutralised five violent extremists and arrested 81 suspected oil thieves.
"The air component destroyed several illegal refining sites in different locations in Rivers," Mr Buba said.
South-east Udo Ka Operation frustrated the activities of the terrorist group and restored peace to troubled areas across the zone.
"The troops have in the month of May, neutralised 69 terrorists, arrested 115 suspects, rescued 32 kidnap hostages, and recovered eight AK47 rifles and 13 pump action guns.
"Overall, troops operations have denied the terrorist the ability to carry out major offensive and has significantly diminished their offensive capability," he said.