ISIL members attacked an Iraqi police checkpoint near the southern city of Najaf, killing seven policemen as government forces in the north made more gains against the fighters in Mosul, their last major stronghold in the country.

The Najaf attack, which involved gunmen and a suicide car bomb, followed blasts a day earlier in Baghdad that left 29 people dead, a reminder of Islamic State of Iraq and the Levant's continued ability to operate away from territory under its control.

The attack near Najaf, 500km south of Mosul and 180km south of Baghdad, happened when two vehicles travelling through the desert were stopped at a police checkpoint around al-Qadisiya town, local police sources said.

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The driver detonated an explosive load and the second vehicle fled. Police pursued it and killed the two assailants inside.

"The security forces fought back, killing the attackers and blowing up the car," an interior ministry statement said.

"They were planning to head to Najaf to blow themselves up there," interior ministry spokesman Saad Maan said, referring to the holy Shia city 40km to the north.

In a statement distributed online by supporters, ISIL claimed responsibility for the attack, which also wounded 17 people, including civilians. It said four gunmen had opened fire before detonating explosive vests, and then a fifth assailant launched a suicide car bomb.

It was not immediately possible to reconcile those accounts.

Attacks in the overwhelmingly Shia south of Iraq are rare, but there have been infiltrations from the western desert of Anbar in recent months.

Najaf is considered a religious capital for Iraq's Shia majority and has always been seen as a major potential target for ISIL, which views Shia Muslims as heretics.

Mosul battle

The recapture of Mosul would probably spell the end for the group's self-styled caliphate in it areas seized in 2014, but ISIL would still be capable of fighting a guerrilla-style insurgency in Iraq, and plotting or inspiring attacks on the West.

Since the US-backed offensive began on October 17, elite forces have retaken a quarter of Mosul in the biggest ground operation in Iraq since the 2003 US-led invasion that toppled Saddam Hussein.

Prime Minister Haidar al-Abadi has said the group would be driven out of the country by April.

The second phase of the campaign launched on Thursday, following weeks of deadlock, has pushed ISIL out of several more areas despite fierce resistance.

The fourth day of the renewed push saw incremental advances on the eastern and southeastern fronts.

A military statement said the counterterrorism forces had retaken part of Karama district.

A federal police officer said Iraqi forces had taken near total control of Intisar and Siha neighbourhoods, and were clearing Salam.

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Iraqi forces have retaken around two-thirds of the eastern half of Mosul from ISIL since the start of the offensive, a top commander said Sunday.

"From east Mosul ... more than 60 percent" has been retaken, Staff Lieutenant-General Abdulwahab al-Saadi, a top commander in Iraq's Counter Terrorism Service (CTS), told AFP news agency.

Although the fighters are vastly outnumbered in Mosul, they have dispersed themselves among residents, hindering Iraqi forces who are trying to avoid civilian casualties. Despite food and water shortages, most civilians have stayed in their homes, rather than fleeing as had been expected.

Thousands more people have fled their homes since the military's new push began, many under the cover of darkness to avoid detection by ISIL.