Iraqi forces, backed by US-led air alliance, have killed 747 Islamic State fighters near Mosul since a massive offensive to recapture the second largest city in Iraq began this month, a senior security official said on Sunday.

Mosul is one of the key strongholds of Islamic State militia.

The chief of Iraq's federal police Raed Jawdat added that the militants had been killed in fighting south of Mosul.

"Around 1,400 square kilometres have been liberated on the southern front where also 88 Daesh fighters have been detained," he said at a press conference, using an Arabic acronym for Islamic State.

The official did not give a figure for casualties among Iraqi forces.

Government forces on Sunday recaptured the village of Rash, 7 kilometres south of Mosul, from Islamic State and raised the Iraqi flag there, the army said in a statement without giving details.

On October 17, government forces, Kurdish troops and Sunni fighters, backed by US-led airpower, started a long-awaited campaign to liberate Mosul.

A powerful pro-government Shiite militia on Saturday started an operation west of Mosul aimed at tightening the noose on the city and cutting off the militants' supply lines between Mosul and areas under their control in neighbouring Syria.

Mosul has been under Islamic State control since mid-2014.

In recent weeks, Islamic State has stepped up attacks in several Iraqi areas, including the capital Baghdad, in response to the Mosul campaign.

At least four people were killed on Sunday in a car bombing in a mostly Shiite area in Baghdad, police and witnesses said.

The bomb in the parked car went off in a commercial street in the northern district of Hurriyah, injuring 10 people.

No one has claimed responsibility for the bombing.

Islamic State claimed similar attacks in the past inside Shiite-majority areas whom the extremist group regards as heretics.

In recent months, Islamic State has suffered military setbacks and lost ground in Iraq.