"Our ground commanders have assured that the end is nearly there", military spokesman Restituto Padilla told reporters.
Up to 90 percent of Marawi's people have fled to safety amid the intense fighting, and rescuers in ambulance vans have crisscrossed the city in recent days to save hundreds of trapped residents.
President Duterte imposed martial law in Mindanao on May 23 following the attack on Maute group militants, which the Philippine leader said were trying to establish a caliphate for worldwide terrorist group IS.
"We are asking your help to please give what your enemies are asking for", the priest said on a video clip shown on a Telegram channel used by Islamic State.
"Mr. President, if you want me to kneel before you just to knock your heart in favor of our families who are crying out there in different places, for our relatives ... we will do that", the priest said.
The militants had killed at least 19 civilians, while 20 security forces and 65 gunmen had died, according to the military.
President Rodrigo Duterte presides over a special Cabinet meeting on martial law attended by Senate President Aquilino Pimentel III and House Speaker Pantaleon Alvarez in Davao City.
On Monday, Padilla said that troops were in "complete control of the city except for certain areas".
"Yes indeed, there was planning involved", Padilla said.
Moreover, upon learning about this terror-related collaboration, Duterte also sought the support of three revolutionary organizations to fight the militant groups in Marawi and nearby municipalities in Lanao Province.
Security experts believe extremists in the southern Philippines have quietly become better organised and funded, pointing to the Maute's rapid rise from obscurity.
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Over the past week, the fighters have shown their muscle, withstanding a sustained assault by the Philippine military and increasing fears that the Islamic State group's violent ideology is gaining a foothold in this country's restive southern islands, where a Muslim separatist rebellion has raged for decades.
"For the terrorists, not surrendering will mean their sure death", he said.
"Despite numerous attempts to reach out to the Maute (militants), they refused to have a stand down in order to evacuate civilians", Galvez said. Later the Cathedral and other churches in the city were torched, and the city has been taken over by the jihadists.
On May 24, the Catholic Bishops' Conference of the Philippines confirmed that Suganob, along with others, was taken hostage by the Maute group following clashes that erupted the day before.
The Islamic State terrorists overrunning Marawi, a city of some 200,000 on Mindanao, are members of a terrorist organization known as the Maute group.
He was being protected in Marawi by the local Maute group, which has pledged allegiance to IS.
Soldiers have taken control of about 70 percent of Marawi, where the gunmen have been fending off the army for a week, military chief of staff Gen. Eduardo Ano said.
Some residents are forced out of their houses by the soldiers who kicked in their doors, the photographer said.
"I have to rescue my grandfather even at the risk of my life", Khana-Anuar Marabur Jr. said Monday after police stopped him for speeding through a checkpoint.
The discovery confirms days of speculation that Maute rebels had killed civilians during a bloody takeover of Marawi City, that the military believes is aimed at winning the Maute recognition from the Islamic State group in the Middle East as a Southeast Asian affiliate.