The insurgents have withstood a relentless US-backed bombing campaign and intense ground battles with troops that have left large parts of Marawi resembling devastated cities in war-torn Syria and Iraq.
Hapilon and Maute members pledged allegiance to terror group ISIS.
The militants have proved to be highly trained and equipped and had meticulously planned the siege, including building a network of tunnels and secretly smuggling in large quantities of weapons and supplies.
Military operations are expected to continue to flush out remaining fighters inside the battle zone.
Seventeen more hostages of the Maute Group, including a five-year old boy, were rescued early Monday, Col. Romeo Brawner, deputy commander of Task Force Ranao said. "Until now our troops are still assaulting the defensive positions of the Maute-IS, and despite the fact that we have set today as a target day for finishing the armed conflict, our troops are still pushing hard, fighting hard to meet this target", Brawner said.
Lorenzana said he and President Rodrigo Duterte postponed a trip to Marawi on Monday when troops informed them an operation to kill Maute and Hapilon was in place.
IS militant Omarkhayam Romato Maute described himself on Facebook as a "walking timebomb".
Photos from ABS-CBN sources show the cadavers of Isnilon Hapilon and Omar Maute.
Those leaders have been central to the rebels regrouping, re-arming and recruiting after previous clashes over the past two years on the southern island of Mindanao.
Their deaths will be a major win for the military, which has been criticised for its slow progress in retaking Marawi, the country's only Muslim majority city, and the ease at which rebels laid siege to it on May 23.
Australia is the only country aside from the United States which has a defence pact with the Philippines that allows its forces to train in the country.
Indonesia, Malaysia and the Philippines have begun coordinated air patrols.
Steelers' Bryant requests to be traded
He had only three targets in the Steelers' win against the Chiefs Sunday, finishing with two catches for 27 yards. Antonio Brown is Pittsburgh's clear No. 1 receiver, but Bryant hasn't been the consistent No. 2 option.
Multiple people injured during Louisiana oil rig explosion
The city of Kenner, in an update on its Facebook page earlier, indicated cleaning chemicals had ignited in the platform. The platform is used to transfer and store oil from nearby wells, and is not a wellhead itself, officials said.
Rams ride defense, special teams in win over Jaguars
The final tally after this sequence: 178 yards, 25 seconds, 14 points, two plays (or three, if you count the touchback). The club will stay in the Jacksonville area this week before flying to London to face the Cardinals for Week 7.