The fighting in Marawi, a mostly Muslim-populated city of 200,000 people, erupted on Tuesday afternoon after security forces raided a house.
"Father Chito Suganob and others were in the Cathedral of Our Lady Help of Christians when members of the Maute fighting group forced their way into the Cathedral, taking with them Fr. Chito and others as hostages," Catholic Bishops' Conference of the Philippines president archbishop Socrates Villegas said in a statement.
"They have threatened to kill the hostages if the government forces unleashed against them are not recalled."
Duterte announced on Tuesday night that martial law had been imposed across the southern region of Mindanao, after Islamist militants rampaged through the city of Marawi and engaged in deadly clashes with security forces.
The fighting in Marawi, a mostly Muslim-populated city of 200,000 people, erupted on Tuesday afternoon after security forces raided a house where they believed Isnilon Hapilon, a leader of the infamous Abu Sayyaf kidnap gang and Philippine head of the Islamic State group, was hiding.
The United States regards Hapilon as one of the world's most dangerous terrorists, offering a bounty of $5 million for his capture.
More than 100 gunmen responded to the raid by burning buildings and conducting other diversionary tactics, according to Defence Secretary Delfin Lorenzana.
Security analysts say Hapilon has been trying to unite Filipino militant groups that have professed allegiance to IS.
These include the Maute group, named after two brothers who lead it and which is based near Marawi.
"We call on the Maute group that claims to bear arms in the name of a Merciful and Benevolent God — the very same God we Christians worship and adore — to do the One God true honour by the mercy and benevolence that are two of our God’s most exalted attributes," Villegas said in the statement.
"At the time of his capture, Fr. Chito was in the performance of his ministry as a priest. He was not a combatant. He was not bearing arms. He was a threat to none. His capture and that of his companions violates every norm of civilised conflict."
Police and military spokesmen were not immediately available to comment on Villegas's report of the hostage taking.