More than 70 Islamic State fighters, including the group's leader in Fallujah, have been killed in US-led coalition airstrikes on the Iraqi city.

American military spokesman Colonel Steve Warren, based in Baghdad, said IS fighting positions were destroyed in 20 strikes over four days.

He also said Maher al-Bilawi, the group's Fallujah commander, had died in the aerial attacks on the besieged city.

"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 said.

"The airstrikes are almost constant," one man told journalists from inside the city".

The resident, who spoke on condition of anonymity, said after living for weeks on rice, canned food and processed cheese, those stocks were beginning to run low.

Fleeing the city

Tens of thousands of civilians have been told by Iraq's government to flee the city, which has been under IS control since 2014.

The spiritual leader of Iraq's Shiites called on Iraqi forces battling to retake the city of Fallujah to protect civilians.

Grand Ayatollah Ali al-Sistani said that "saving innocent people from harm's way is the most important thing, even more so than targeting the enemy".

Iraqi troops have been trying to drive IS militants from their stronghold west of Baghdad after launching the new offensive on Sunday night, and US planes have dropped leaflets telling locals to avoid IS areas.

Col Warren said: " "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".