CNN Philippines correspondent David Santos, who is currently less than five kilometers from the fighting, said the progress of government forces has been slowed by concerns over civilians caught in the crossfire.
About 1,000 civilians remain trapped in the war-torn city, according to the city's mayor.
A number of militants were taking shelter in the city's mosques, using their characteristic minarets as sniper positions, said Santos. The fighting has so far claimed the lives of 58 government troops and over 100 civilians.
Duterte: Baghdadi ordered attack
Philippine President Duterte told reporters Sunday the attack on Marawi had been ordered directly by the leader of ISIS, Abu Bakr al-Baghdadi.
The president made his speech while visiting wounded troops in Cagayan de Oro City, in northern Mindanao. Later, in Manila, he watched dead soldiers return from the front lines.
"Now it appears al-Baghdadi himself, the leader of the ISIS, has specifically ordered terroristic activities here in the Philippines," Duterte claimed, attributing it to information he'd received from his security officials. The Filipino leader didn't provide any additional evidence.
Meanwhile the status of two leaders of an ISIS-affiliated militant group, Omar and Abdullah Maute, was unknown on Monday morning, amid reports they'd been killed.
Duterte also claimed the siege of Marawi was not triggered by religious extremism but rather by "illegal drugs trade."
"Rebellion was financed by drug money. It has nothing to do with religion. I refuse to believe that it is religion that fueled this war," he said.
How it began
The militants set fire to churches and other buildings as they entered the city, while ISIS' media wing, Amaq Agency, put out a statement announcing that "fighters of the Islamic State launch a wide-scale offensive on positions of Philippine troops in the city of Marawi."
The siege on Marawi unfolded as Muslims worldwide began to mark the holy month of Ramadan. Mindanao has a significant Muslim population, though the Philippines is a predominantly Catholic country.
Confusion over US support
There were conflicting reports over the weekend from Duterte and the US Embassy in Manila over whether US support had been requested in the Marawi fight.
US forces were providing "technical assistance" to Philippines troops fighting ISIS militants in the southern city, Presidential Spokesperson Ernie Abella confirmed Sunday.
However Abella stressed on Sunday US involvement in the fight for Marawi was very limited. "It does not involve any boots on the ground nor is there any direct participation in combat operations, a matter prohibited by law," he said.
Speaking to reporters Sunday, Duterte said no request of assistance had been made to US forces. "I was not aware of that until they arrived ... I never approached any American to say that 'please help us'," he said.
The number of troops there ranges between 50 to 100 at any given time, the Pentagon said.