Coalition airstrikes on the western Iraqi city of Fallujah have killed more than 70 Islamic State fighters, including the local commander, the Pentagon said Friday.

The commander killed was identified as Maher al-Bilawi. Pentagon spokesman Army Colonel Steve Warren said al-Bilawi was killed two days ago in an example of how the coalition is "continuously chipping away at leaders."

While the death of al-Bilawi was positive for the coalition, it is unclear how long the battle for Fallujah will last, Warren told reporters from Baghdad. There are still up to 50,000 citizens remaining in the city 50 kilometres west of the capital Baghdad.

"The Iraqi government has been clear that protecting these civilians is their priority," Warren said.

The coalition has dropped leaflets informing the population to avoid Islamic State areas and directing people who cannot leave to put white sheets on their roofs to mark their locations. The Iraqi army is working to establish evacuation routes, and the local Anbar government has set up camps for displaced civilians, Warren said.

Iraq's top Shiite cleric Ali al-Sistani earlier Friday called for the protection of civilians trapped in Fallujah by Islamic State amid fears they are bearing the brunt of an ongoing offensive.

"Saving an innocent human from harm is more important and greater than targeting the enemy," al-Sistani's representative, Ahmed al-Safi, said in a sermon at a mosque in the holy city of Karbala, according to independent website Alsumaria News.

On Monday, Iraqi government forces, backed by a powerful Shiite militia and US-led airstrikes, started an onslaught to dislodge Islamic State from its stronghold in the mostly Sunni city of Fallujah.

The civilians who remain trapped are prevented from escaping by the extremists as the city continues to come under heavy bombardment from Iraqi forces, the UN High Commissioner for Refugees (UNHCR) said on Friday.

The coalition has been supporting the fight to retake Fallujah with artillery in addition to the airstrikes, Warren said. Twenty strikes over the last four days have destroyed fighting positions and gun emplacements.

In December 2015, routes out of the city were cut off and civilians prevented from leaving, according to the agency. 

Since then, food and medicines have been in short supply, and families have had to rely on unsafe water sources.

Fallujah was the first Iraqi city to fall to Islamic State, before the radical Sunni group seized more territory in the country in a lightning attack months later.

Islamic State still controls key areas in Sunni Arab northern and western Iraq, including Mosul, the country's second-largest city.

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