Philippine Defense Secretary Delfin Lorenzana said Isnilon Hapilon, the alleged emir of the IS jihadist group in Southeast Asia, and Omarkhayam Maute were killed in a firefight Monday morning.
"Crumbling leadership signals the beginning of the end", said Marawi City Bishop Edwin dela Peña in an interview.
Government troops are now chasing a foreign terrorist who is fighting on the side of the Maute group in the city. Washington had offered a reward of five million dollars for any information for the arrest of Hapilon.
Hapilon, who is listed as one of the FBI's most-wanted terror suspects, and Maute have always been in the crosshairs of the Philippine state.
"We will announce the termination of hostilities once government forces have ensured that there are no more terrorists-stragglers in the city and we have cleared all structures of IEDs and other traps", he added.
Lorenzana said the killings of Hapilon and Maute mean that the Marawi conflict will be over soon and that the government will soon announce the "termination of hostilities in a couple of days".
The military previously estimated that they will liberate Marawi by Sunday.
Lorenzana also disclosed that President Rodrigo Duterte was scheduled to visit Marawi again on Monday but said they were "prevailed by the commanders on the ground to postpone the trip because they are going to conduct the assault this morning".
The reports cited state security officials who are familiar with the battle in Marawi, which began in May.
Lorenzana said once fighting stops, "We will refocus our efforts on the challenging task of rebuilding and rehabilitating Marawi".
In 2004, the group bombed a passenger ferry in Manila Bay, killing 116 people, while in 2014, Abu Sayyaf militants attacked civilians celebrating the end of Ramadan, in Talipao, in Sulu province in the far south west of the country, killing at least 21, according to the US State Department.
Local assemblyman Zia Alonto Adiong said that with the death of two militant leaders involved in the siege, the eagerness of the more than 390,000 displaced residents to return home is mounting.
With major terrorists eliminated, Zubiri said that rehabilitation, resettlement and development activities can go "full blast".
At the press conference, aired live nationwide, Lorenzana, said Malaysian national Dr. Mahmud, Ahmad, a Universiti Malaya professor who joined the Islamic State and is believe to have been among those who planned the Marawi siege, is reportedly still hiding in one of the buildings there.
Lorenzana said martial law will not be lifted yet. However, with regard to the lifting of the martial law, he said the situation will be assessed thoroughly before a decision was taken.