The clashes come a day after Iraqi and Kurdish troops backed by US air strikes dislodged Islamic militants from a strategic dam in the country’s north.
They began on the south-western outskirts of the militant-held city of Tikrit, located about 80 miles north of the capital, when a military convoy was travelling along the main highway that links Baghdad with the northern provinces.
The Iraqi military shelled militant positions inside and outside the city. There were no immediate reports of casualties.
Sunni extremists from the Islamic State group have occupied Tikrit and the northern city of Mosul since early June, as well as large parts of the country’s north and west. The militant onslaught has plunged Iraq into its worst crisis since the withdrawal of US troops in 2011.
The group has since imposed its own harsh interpretation of Islamic law in territory it controls in Iraq and neighbouring Syria.
Sporadic clashes have been reported around Tikrit and other areas since then, but efforts by Iraqi government forces and allied Sunni tribal militiamen have failed to push out the militants. Earlier this month, the tomb of former Iraqi dictator Saddam Hussein located near Tikrit was damaged in clashes between security forces and the radical group.
On Monday, Iraqi and Kurdish forces recaptured Iraq’s Mosul Dam less than two weeks after it was seized by the militants. The dam is the largest in Iraq and a vital power and water resource for the country.
The gains made by the militants brought US forces back into the conflict for the first time since they withdrew in 2011.