Qassim Abdul-Zahra?and Sinan Salaheddin

CAMP TARIQ, IRAQ: Elite Iraqi special forces began their push Monday into Fallujah, expecting to encounter the stiffest resistance yet in the campaign to free territory from the Islamic State group.

The city 40 miles west of Baghdad has been under militant control longer than any other part of Iraq, and IS fighters have had more than two years to dig in. Networks of tunnels like those found in other IS-held territory have already been discovered in its northeastern outskirts.

The Iraqi troops, also known as the counterterrorism forces, are leading the assault on Fallujah, slowly moving up from the southern edge in a column of armored Humvees.

Their advance is expected to be slow because tens of thousands of civilians remain trapped in Fallujah and hidden bombs are believed to have been left throughout the city, according to special forces commanders at the scene. They expect fierce resistance from the jihadis, who have nowhere to run.

“This is the decisive battle for us and for Daesh,” said Gen. Saad Harbiya, head of Fallujah operations for the Iraqi army, using an Arabic acronym for the Islamic State group.

The offensive, supported by airstrikes from the U.S.-led coalition, was launched a week ago. In that time, other wings of Iraq’s security forces have cleared the city’s edges. Shiite militia forces under the government umbrella of the Popular Mobilization Forces and the federal police led operations that have taken back 80 percent of the territory around Fallujah, according to Iraqi Maj. Dhia Thamir.

The predominantly Sunni city in Anbar province is one of the last major IS strongholds in Iraq. The extremist group still controls territory in the north and west, as well as the second-largest city of Mosul.

Harbiya said Fallujah “is like the Kaaba” for the Islamic State group, referring to the most sacred Muslim site in the world in Mecca, Saudi Arabia.

The 500-700 IS fighters holed up in Fallujah are expected to be some of the group’s best-trained, a special forces commander at the scene said. The commander spoke on condition of anonymity because he was not authorized to brief reporters.

Islamic State extremists, meanwhile, claimed responsibility for a wave of bombings Monday in and around the capital that killed at least 24 people.