The militants called for reinforcements and around 100 gunmen entered Marawi, a mostly Muslim city of 200,000 people on the southern island of Mindanao, Defense Secretary Delfin Lorenzana said.
He also heads an alliance that includes at least 10 smaller militant groups, including the Maute, which have a heavy presence in Marawi and were instrumental in fighting off government forces in this week's battles.
Authorities said ending the crisis was proving extremely hard because the militants were holed up in residential buildings, had planted improvised bombs in the streets and had taken Catholic hostages.
The current martial law order - which covers both the city of Marawi and the wider island of Mindanao, of which Marawi is a part - came after deadly clashes broke out between Filipino government troops and Islamist militants Tuesday.
The southern Philippines, particularly the resource-rich but poverty-wracked Mindanao region, has always been a hotbed of activity by the Abu Sayyaf and other fundamentalist groups. The US regards Hapilon as one of the most risky terrorists in the world, offering $5 million for his capture.
A woman touches an image of Jesus Christ shortly after attending a mass for victims of the recent attack in Marawi by Muslim militants linked to the Islamic State group and also for extrajudicial killings inside a church in Man.
Duterte said a local police chief was stopped at a militant checkpoint and beheaded.
Apart from the imposition of Martial Law, the CPP slammed the severe measures ordered by the President to the military such as to carry out searches and warrantless arrest, impose curfews, establish checkpoints and other restrictions which, according to CPP, violates people's freedom of movement.
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"Our operation is still ongoing in Marawi City and sporadic fighting is still continuing", a statement from the Armed Forces of the Philippines said.
Should Philippine President Rodrigo Duterte implement nationwide martial law, as recently suggested, many fear an abuse of power as alleged political suppression and rights violations already dog his administration.
The military claimed to have killed at least 13 fighters, members of groups that have pledged allegiance to the Islamic State of Iraq and the Levant (ISIL) group.
But Aquino said he decided against it partly because military rule could spark resentment among local people.
Mr Mayormita said he had not been able to contact his wife since then. It was not clear what exactly Duterte planned to do to achieve that once the Marawi siege ends.
Duterte submitted to Congress on Thursday the proclamation of martial law for review as required by the constitution.
MANILA-The National Food Authority (NFA) assures the public that there is enough rice in Marawi City, which is now being gripped by a running gun battle between government troops and the Maute terrorist group.
The country suffered 14 years of martial law under former dictator Ferdinand Marcos, who was ousted in a peaceful revolution in 1986.
"I will not hesitate to do anything and everything to protect and preserve the Filipino nation", the president said.