An Iraqi prominent Shiite militia leader was killed in battles to free the city of Tikrit, capital of Salahudin province, from the Islamic State (IS) militants, a security source said on Sunday.

Ali al-Mosawi, also known as Abu al-Hasanien, the commander of Imam Ali Brigades, was killed late on Saturday night in battles between his militiamen and the IS militants at the western edge of Tikrit, some 170 km north of the Iraqi capital of Baghdad, the source told Xinhua on condition of anonymity.

Al-Mosawi was a member of the Iraqi National Assembly which was formed in 2005 after the US-led occupation of Iraq in 2003.

His Imam Ali Brigades' group is part of the government-backed Hashid Shaabi, or Popular Mobilization, paramilitary groups.

Al-Mosawi's killing came ten days after the killing of Nouri Abu Mahdi, a prominent leader of a Shiite militia known as "Asa'ib Ahl al-Haq", who was also killed in Salahudin province when a roadside bomb struck his vehicle near the town of Dour, in south of Tikrit.

Imam Ali Brigades and Asa'ib Ahl al-Haq, or League of the Righteous, are allegedly funded, trained and armed by Iran's Quds Force during the US occupation of Iraq and later became allied to the Shiite-led government in Baghdad.

The incident occurred as the Iraqi troops and government-backed Shiite and Sunni militias have been carrying out an offensive since Tuesday to free Tikrit and gained some ground in parts of the city.

However, they have been moving slowly and cautiously amid heavy clashes with the militants, including a large number of IS snipers, while they also have to deal with hundreds of roadside bombs and booby-trapped houses.

On Saturday, Karim al-Nouri, a leading figure of the Shiite party Badr Organization and the spokesman of the government-backed militia of al-Hashed al-Shaabi, said that the city "will be liberated within 72 hours."

Some 30,000 Iraqi troops and thousands of allied Shiite and Sunni militias have been involved in 12-day-long operation to recapture Tikrit and other key towns and villages in the northern part of Salahudin province from IS militants.

Large parts of the province have been under IS control since June 2014, after bloody clashes broke out between Iraqi security forces and the group.

The IS has taken control of the country's northern city of Mosul and later seized swathes of territories in Nineveh and other predominantly Sunni provinces.