Operation Fallujah: A 'tough nut to crack' says minister
Fallujah, which is located in Iraq's Anbar province, was the first of the country's cities to fall to the IS group in January 2014.
An operation to recapture the city from IS militants took off last month with the Iraqi army leading the offensive backed by Shia militias known as the Popular Mobilisation Forces [PMF].
"Fallujah is a tough nut to crack," Hoshyar Zebari said during an interview with Reuters news agency on Thursday evening.
"Daesh are holding the population as hostages, not allowing them to escape and they are putting up a tough fight there," he said using the Arabic acronym for IS.
The fight for Fallujah is expected to be protracted as IS have had more than two years to dig tunnels and plant hidden bombs across the city.
"Nobody can give you a definitive time when Fallujah will be cleared of Daesh," Zebari said during the interview, "Mainly because of the resistance, because of the IEDs [improvised explosive devices], because of the tunnels" dug by the militants to enable clear undetected movement.
"The [Iraqi] security forces and the PMF have made significant progress but really to storm the centre of Fallujah I think will take time," Zebari added, "We should not declare victory prematurely."
Iraqi Prime Minister Haider al-Abadi announced on Wednesday that the offensive against IS has been temporarily slowed over fears for the safety of the city's civilian population currently trapped there.
His comments came after the UN warned that IS militants could be using hundreds of Iraqi families as human shields in the fight.
Only 5,000 civilians of the 50,000 trapped in the city have managed to escape, many of whom walked for hours and came under fire as they fled.