In the past year the administration of President Rodrigo Duterte has been engaged in an on-and-off truce with the communist rebels.
The Palace is trying to assuage the public but says there is no clear timeline as yet for lifting the martial law in Mindanao.
The Philippines military said it arrested one of the Maute brothers on Thursday, a senior member of the Islamic State-backed militants it is fighting in a southern city.
The Philippine Daily Inquirer reports that De Lima issued a written statement from her cell in a Manila prison.
Duterte placed the whole Mindanao under martial law last May 23 after Islamic State-inspired Maute terrorists attacked Marawi to protect Abu Sayyaf leader Isnilon Hapilon from government forces. "The public deserves nothing less".
Responding to reporters' queries about Duterte's remarks, presidential spokesperson Ernesto Abella said Sunday: "The President's media interview yesterday after visiting the troops in Butuan underscores that he adheres to the rule of law and judicial independence".
Although the compound is secured by the military, it is only about two kilometres from the pockets of the city that the gunmen control.
Philippine President Rodrigo Duterte said on Saturday that the Philippine forces are now facing a formidable and ferocious Islamist militants who are out to kill "all nonbelievers".
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The militants remain holed up in pockets of Marawi alongside hundreds of trapped civilians being used as hostages or human shields.
"I'm saying that there's nothing to worry about in terms of sickness", he said.
A rested Duterte attended an event honoring soldiers killed in Marawi City.
A total of 19 deaths have been registered among those displaced by the fighting, said Mujiv Hatama, the governor of the Autonomous Region in Muslim Mindanao (ARMM), who said severe dehydration from diarrhea was the main cause of death.
Duterte's anti-terror offensive has shifted the spotlight from his controversial anti-drug campaign that has dominated headlines since he entered office almost a year ago, but Dominguez insisted that both matters were intertwined.
Their parents were taken into custody last week in separate cities.
He said then his doctor made him stop using it on learning he was "abusing the drug" by using more than the prescribed amount.
Under the constitution, the separately elected vice president shall act as president if the incumbent dies, is permanently disabled or removed from office.