Maute was the leader of the Maute group, which was founded by him and his brother Abdullah.
The reports cited state security officials who are familiar with the battle in Marawi, which began in May.
"We were supposed to go to Marawi with the President but we were prevailed upon by the commanders on the ground to postpone our trip because they are going to conduct the assault today", Lorenzana told reporters in a chance interview in Camp Aguinaldo, Quezon City.
Lorenzana said IS Southeast Asian "emir" Isnilon Hapilon and Omarkhayam Maute were among the fatalities in the early morning fighting. Gen. Restituto Padilla said yesterday.
Filipino government troops on a truck manoeuvre at a deserted street as fighting between Islamist militants and government forces continues in Marawi City, Mindanao Island, southern Philippines, 02 June 2017.
Less than eight of their foreign companions, including Malaysians and Indonesians, are left on the battlefield backing the remaining Maute and Abu Sayyaf fighters.
He said the 4ID is in close coordination with the Armed Forces of the Philippines' Western Mindanao Command for any intelligence update regarding the movement and presence of the remaining insurgents.
The Philippines military is about to end the long battle of Marawi where an Islamic State-linked terrorist group is making its "last stand" amid heavy fighting, top army commanders announced, according to AFP.
Ahmad is also reported to be a university lecturer in his home country in charge of raising finances from overseas for the jihadists and recruitment.
Security officials believe Hapilon's death is significant, considering he was the uniting factor in Marawi, and that the blow to the worldwide terror network is also serious, especially since the he was named by Daesh as emir of Southeast Asia.
The military said Monday Hapilon - on the United States "most wanted terrorists" list - was killed in a dawn offensive alongside Omarkhayam Maute, one of two brothers who with Hapilon plotted to take over the city. More than 1,000 people have been killed, including about 800 militants.
It is only a matter of time before Abu Sayyaf proclaims a replacement for their slain leader, Isnilon Hapilon, a Muslim scholar said Tuesday.
Padilla said troops were trying their best to make Marawi safe from bombs and booby traps.
On the issue of lifting martial law, Lorenzana said a recommendation would be made to President Duterte before the end of the month.