Islamic State is putting up a tough fight in Falluja and its recapture by the Iraqi army could take time, said Iraqi Finance Minister Hoshiyar Zebari.
Falluja, located 50 kilometers (32 miles) west of Baghdad, has been a bastion of the Sunni insurgency that fought both the U.S. occupation of Iraq and the Shi'ite-led Baghdad government.
Islamic State fighters raised their flag there in January 2014 before sweeping through much of Iraq's north and west, declaring a caliphate several months later, from Mosul.
"Falluja is a tough nut to crack," he told Reuters in an interview 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 added, referring to the militant group by one of its Arabic acronyms.
"Nobody can give you a definitive time when Falluja will be cleared of Daesh. Mainly because of the resistance, because of the IEDs (improvised explosive devices), because of the tunnels" the militants have dug to move without being detected, he added.
The army started the offensive on May 23, with the backing of Shi'ite militias known as Popular Mobilization Forces (PMF) and air support from the U.S.-led coalition.
Prime Minister Haider al-Abadi said on Wednesday the army had slowed the pace of its offensive because of fears for the safety of tens of thousands of civilians trapped in the city with limited access to water, food and healthcare.
"The security forces, the PMF have made significant progress but really to storm the center of Falluja I think will take time," Zebari said. "We should not declare victory prematurely."
A spokesman for one of the main Shi'ite paramilitary groups taking part in the offensive on Falluja said the operations have come to a near standstill in the past three days and asked Abadi to order the attacks to continue.
"We demand that Prime Minister Abadi continues the operation to free Falluja and not to submit to American and Western pressure to halt the operation," said Jawad al-Talabawi, a spokesman of the Iran-backed Asaib Ahl al-Haq.
"We say ... freeing Falluja is needed to protect Baghdad."
Abadi ordered the offensive on Falluja after a series of bombings claimed by Islamic State hit Shi'ite districts of Baghdad, causing the worst death toll this year.
Falluja would be the third major city in Iraq recaptured by the government after former dictator Saddam Hussein's home town Tikrit and Ramadi, the capital of Iraq's vast western Anbar province. Abadi has expressed hope that 2016 will be the year of "final victory" over Islamic State, with the capture of Mosul, their de facto capital in northern Iraq.
Baghdad-based political analysts said the battle for Falluja would be harder than Tikrit and Ramadi because of the symbolism of the city for the militants and because they cannot retreat to other places, as the whole area is under siege by the army and Shi'ite militias.
"In Falluja, Daesh has die-hard fighters defending a city they consider as a symbol for Jihad," said analyst and former army general Jasim al-Bahadili.
Political analyst Ali Hashim said that even if the government managed to retake Falluja, it would continue to face the problem of winning over the Sunni population, some of whom feel marginalized by the Shi’ite-led government.