"As follow-up and clearing operations continue, we expect the enemy to yield more previously occupied positions, but not without a fight", he said.
Security forces have engaged in ferocious street to street combat and launched airstrikes in their efforts to expel the fighters from the city of Marawi.
This photo, taken on July 22, 2017, shows an army soldier on patrol in a deserted neighborhood of Marawi, in southern Philippines.
Col. Romeo Brawner, deputy commander of the task force battling the militants, said the military had encountered some of the heaviest resistance in recovering the mosque.
"We have not seen him yet and don't know where he is for now and if he will be brought to Marawi or Manila", Galido said.
"They are retreating while we are assaulting but in the process of doing so, we are encountering many improvised explosive devices so we can not just advance".
"It's very important that we get their leaders so there will be no repeat of what happened in Marawi".
Brawner said one soldier was killed and seven were wounded in the battle to push the terrorists out of the mosque.
In a phone interview with Rappler, Dureza said Soganub was rescued near Bato Mosque.
Military spokesperson Brig. Gen. Restituto Padilla meanwhile told ABS-CBN News that he could not yet confirm the news pending official reports from Marawi troops. Defense Secretary Delfin Lorenzana estimated that it would take more than 50 billion pesos ($1 billion) to rebuild Marawi, a scenic lakeside city of about 200,000 people before the siege.
Presidential spokesman Ernesto Abella said the Palace will provide information on the war in Marawi City "as soon as conditions on the ground allows".
Marawi Bishop Edwin dela Peña on Sunday expressed delight after learning about the rescue of Catholic priest Teresito "Chito" Suganob.
Suganob escaped on Saturday evening after government forces reclaimed the mosque where the priest was being held captive since May 23.
The rubble-strewn streets were practically empty except for scores of heavily armed soldiers securing the area.
Fighting between state troops and Islamic State-linked terrorists has been raging for almost four months in Marawi, leaving at least 845 dead, a lot of them terrorists, and hundreds of thousands displaced.
More than 800 militants, government troops and civilians have since been killed in the conflict, which has forced thousands to flee their homes and destroyed large parts of the once-bustling city.