The extremists forced their way into St Mary's Cathedral in Marawi, taking Pastor Teresito 'Chito' Suganob, ten worshippers and three church workers hostage before burning down their church.
Thousands of people have since fled the mainly Muslim city in Lanao del Sur province on the southern island of Mindanao. The province is a stronghold for the Maute group, which has pledged allegiance IS.
Andrew Boyd from religious freedom charity Release International told Premier's News Hour the situation is looking bleak.
He said: "The guerrilla group, which is a radical group, which subscribes to the ideology of Islamic State - it wants to see a Caliphate - it wants the Philippines to be part of that - [it] is threatening to kill the hostages unless the government backs off and removes its troops.
"That is unlikely to happen."
The armed men also burned down three buildings of the church-owned Dansalan College on Tuesday.
It comes after government forces failed in an attempt to capture local wanted terrorist leader Isnilon Hapilon, who Philippine Solicitor General Jose Calida says has been designated by IS as its leader in the Philippines.
Gunmen began their rampage on the island, flying IS flags after the failed raid. At least eleven soldiers and 31 militants had been killed.
Boyd added that the fighting in the country is no longer a local or regional issue.
He said: "The government in the Philippines is acknowledging perhaps for the first time that foreign jihadists have been involved in this because some of those killed are including fighters from Indonesia and Malaysia."
President Rodrigo Duterte has imposed martial law in Mindanao in response to the violence.
Click here to listen to Premier's Alex Williams speaking with Andrew Boyd, spokesman for Release International:
