The clashes began on the southwestern outskirts of the militant-held city of Tikrit, located about 130 kilometres north of the capital, when a military convoy was travelling along the main highway that links Baghdad with the northern provinces, they said.
The Iraqi military shelled militant positions inside and outside the city, they said. There were no immediate reports of casualties. Both spoke on condition of anonymity, fearing their safety.
The group since has imposed a self-styled caliphate in territory it controls in Iraq and neighbouring Syria, imposing their own harsh interpretation of Islamic law.
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.
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The gains made by the militants brought US forces back into the conflict for the first time since they withdrew in 2011. America's renewed involvement on the battle field was a reflection of the growing international concern over the Sunni extremist group. Washington began carrying out dozens of airstrikes on August 8.
Hours after retaking the dam, President Barack Obama called the development a "major step forward" in the battle against the group.
"We've got a national security interest in making sure our people are protected and in making sure that a savage group that seems willing to slaughter people for no rhyme or reason other than they have not kowtowed, that a group like that is contained, because ultimately it can pose a threat to us," Obama told reporters.