"Our intelligence suggests one of the four is top neo-JMB (neo-Jamaatul Mujahideen Bangladesh) leader Musa," Police's Assistant Inspector General M Moniruzzaman told PTI.
The army said they have wrapped up their assaults on the militant den by late evening.
"Accomplishing all (our army) actions, the building has been handed over to the police administration as a 'crime scene' this afternoon with announcement of the end of Operations Twilight," army spokesman Brigadier General Fakhrul Ahsan told a news briefing at Sylhet's Jalalabad Cantonment.
Military took one more day to accomplish the required procedures including further security searches and disposal of devices left by the slain extremists, he said.
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"The entire operation was carried out in line with Prime Minister Sheikh Hasina's specific directives," Ahsan said.
The July 1 attack on Holey Artisan Bakery in Dhaka's posh diplomatic area killed 23 people, including an Indian girl.
Meanwhile, Forensic investigation was ordered to further confirm Musa's identity as his face was mutilated in the fierce encounter. Officials earlier identified the man only as Musa, saying he took the charge of the outfit as a massive anti-militancy operations killed several top neo-JMB leaders after the July 1 attack on Holey Artisan cafe.
The four militants, including a woman, were holed up in a building that saw powerful blasts claimed by the Islamic State that killed six people in northeastern Sylhet city.
Bangladesh's army today cleared the booby-trapped militant den in Sylhet and carried out controlled explosions of bombs in the building.
"They (troops) are using drones to get a clearer picture before stepping inside different corners of the building to evade booby traps," an official said.
Sylhet-based 17 Infantry Division's Major General Anwarul Momen was leading the operation, assisted by police's SWAT and counter-terrorism units.
"The militants had kept a bucket filled with explosives at the collapsible gate at entrance of the building. When we detonated them from distance, the collapsible gate was blown out so vigorously, walls of another building several yards away were severely damaged," Ahsan said.
Authorities called out commandos on Saturday morning, two days after a security siege to the building.
On Saturday evening, two powerful bombs ripped through a crowd near the building, killing six people, two being police officers and injuring about 50, including two army officers.
RAB Intelligence Wing chief Lt Col Abul Kalam was seriously wounded in blasts and flown to Dhaka for treatment. He was later flown to Singapore.
Hours later the Islamic State claimed responsibility for the attack through its propaganda news agency 'Amaq'.
The encounter continued into Sunday, when army commandos shot dead two militants at the building. The militants were equipped with small arms, explosives and grenades.
Residents who lived in the house as tenants said they were virtually taken to hostage with militants warning them of bombs implanted on their way out while the commandos brought them out from the top of the building making their way there from the rooftop of an adjacent structure.
Bangladesh has been witnessing a spate of attacks on secular activists, foreigners and religious minorities since 2013. The country launched a massive crackdown on militants specially after the Dhaka cafe attack.