The minister explained that a female hostage who escaped the militants' captivity helped locate Hapilon and Maute in one of the buildings in the main battle area in Marawi city.
Following his appointment, Hapilon, based in Basilan, combined his terror unit with the Maute Group in central Mindanao. One of the terror leaders was on the FBI's list of most wanted terrorists.
The military, which killed two key militant leaders on Monday, said they hoped it was the final phase of defeating a dwindling band of fighters who had occupied Marawi for nearly five months.
Military leaders had said last month that three leaders of the Islamic State-linked militants who besieged the southern city were killed in the months of fighting but the two still alive were leading a final stand. Hapilon also had a $5m USA bounty on his head for carrying out multiple ransom kidnappings and beheadings of United States citizens.
Philippine authorities have made several previous announcements on the imminent end of the conflict, but observers believe this time the forecast is likely to be accurate.
Also known as Abu Handzalah, Mahmud, reports said, is considered as the driving force behind the unity of Abu Sayyaf, Maute Group, BIFF and Ansarul Khilafah Philippines who pledged to fight under the Islamic State.
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Since then more than 1,000 people have been killed and 400,000 residents displaced as insurgents were hit with a relentless bombing campaign and intense ground battles with troops. Duterte has imposed martial law across the southern third of the Philippines to quell the militant threat. Defence chiefs last month said other Philippine militant leaders had been killed in the battle for Marawi.
The military's recent offensive led to the release of 17 hostages, according to Zia Alonto Adiong, spokesperson for the Marawi Crisis Management Committee.
Marawi is Lanao del Sur's capital and largest city.
"We pray for all the dead, and for lasting peace in Mindanao", he added. "This means their centre of gravity has crumbled", he told reporters. He said "the Maute-IS have established very strong defensive positions", adding that the IS fighters were hiding in dugouts and basements of occupied buildings.
However an analyst said the deaths of the leaders would likely prompt retaliatory attacks from their followers and allies, with young leaders seeking to take their place.
Terrorism expert Ahmad Kumar Ramakrishna from Singapore's S. Rajaratnam School of International Studies said if Ahmad survived he would likely take over the leadership of IS-linked fighters in the southern Philippines.