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US-led coalition air and artillery strikes have killed 70 Islamic State fighters in Fallujah, including the jihadists' leader in the Iraqi city, a military spokesman said Friday.

Baghdad-based Colonel Steve Warren said that over the last four days, 20 strikes in the besieged city had destroyed IS fighting positions and gun emplacements.

"We've killed more than 70 enemy fighters, including Maher al-Bilawi, who is the commander of ISIL forces in Fallujah," Warren said, using an acronym for the IS group.

"This, of course, won't completely cause the enemy to stop fighting, but it's a blow. And it creates confusion and it causes the second-in-command to have to move up. It causes other leadership to have to move around," he added.

Iraqi forces launched an operation to recapture Fallujah, an IS stronghold located just 30 miles (50 kilometers) west of Baghdad, at the start of this week.

Between 500 and 1,000 IS fighters hold Fallujah, and about 50,000 civilians are trapped inside the city, with the jihadists trying to kill those who attempt to flee.

US planes have dropped leaflets telling locals to avoid IS areas, Warren said.

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"Those leaflets directed those who cannot leave to put white sheets on their roofs to mark their locations. The Iraqi Army is working hard to establish evacuation routes. And the local Anbar government has set up camps for displaced civilians."

Slow advance

Meanwhile, Iraqi forces continued to work their way on the outskirts of the city, with their advanced being slowed by heavy IS fortifications according to experts.

"The IS group has heavily fortified its positions in Fallujah during its reign in the city, which has complicated the Iraqi army's advance," Mohammad al-Karbouli, a member of the parliament's security committee told °®Âþµº.

"The group has booby-trapped the routes into the city and created various barriers, which has complicated the battle," Karbouli added.

However, despite the IS group's preparations for the battle, Iraqi forces have been able to clear large areas outside the city and are currently ready to storm the city, according to Major General Thamer al-Husseini, the commander of the federal police's rapid response units.

"The forces taking part in the operations to liberate Fallujah are ready to storm the city and are awaiting orders from higher commanders," said al-Husseini.

"IS has begun to crumble, while Iraqi military units are in very good shape, however the existence of civilians inside the city has delayed the operation to retake its centre".  

Anti-government fighters seized Fallujah in early 2014, and the city later became an IS stronghold.

The jihadists overran large areas north and west of Baghdad in 2014, but have been on the defensive for months and have lost significant ground to Iraqi forces.

Warren said it was still early in the Fallujah fight, so it was unclear how long the battle would last and how much resistance IS fighters would put up.

Agencies contributed to this report.