The bloody siege prompted President Rodrigo Duterte to place the entire Mindanao region under martial law and order aerial and artillery bombing of the enemies' positions, sending them into retreat but leaving the city in ruins.
But as life and some traffic resumed in Marawi's outskirts, the sounds of fighting rattled some who returned. "We just needed to get these two (leaders) to make sure the leadership, the centre of gravity falls, and elsewhere even the Maute-ISIS (fighters) in other areas would also crumble".
Brawner said four Maute members were killed and 10 soldiers were wounded in Tuesday's fighting.
Earlier today sporadic gunfire and explosions could be heard in the southern Philippine city as soldiers fought the remaining Islamic militants to gain control of the last pocket of the city.
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He further said that "West has no right to ask why Iran is present in the region, or why Iran has missiles". He has threatened to terminate the Obama-era agreement altogether.
"I promise you this will never happen again", he said as he gave troops a snappy salute.
Military chief General Eduardo Ano said Mr Duterte's statement meant the threat from the militants, who had been fighting in Marawi since May 23, was substantially over.
Marawi, a mosque-studded center of Islamic faith in the predominantly Roman Catholic Philippines, has been devastated by the siege by the militants, who waved IS-style black flags and hung them on buildings they occupied in Marawi's business district and outlying areas, according to the military.
The United States and Australia have deployed surveillance aircraft to help Filipino troops battling the Marawi attackers.
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Eight other foreign terrorists - mostly Indonesians and Malaysians - are believed to be still holed up in Marawi, authorities said.
The surprise occupation of the city and the involvement of foreign fighters set off alarms in Southeast Asia and the West. Analysts said parts of the southern Philippines were at risk of becoming a new base for IS as it lost territory to worldwide forces in Iraq and Syria.
"We have received a report from [Armed Forces of the Philippines] ground commanders in Marawi that the operation conducted by government forces to retake the last remaining Daesh-Maute stronghold in the city has resulted in the death of the last terrorist leaders Isnilon Hapilon and Omar Maute, and that their bodies have been recovered by our operating units", said Lorenzana.
A top Malaysian militant, Mahmud bin Ahmad, who uses the nom de guerre Abu Handzalah and is a close associate of Hapilon, has not been found and was among the remaining militants being hunted by troops, he said. He explained that they want to ensure the safety of the residents of Marawi before being allowed to return to their houses.
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He said the death of these leaders means the fighting is nearly over and they will announce the termination of hostilities "in a couple of days".