Iraqi Shiite paramilitaries position mortars to strike Islamic State group militants north of Fallujah, Iraq, July 6, 2015. Reuters/Stringer

Iraqi Shiite militia fighters are reporting progress in their push to oust Islamic State militants from Fallujah, a strategic city whose capture would mark a significant step in conquering the predominantly Sunni western province of Anbar. Shiite and government fighters this week made gains north of Fallujah during clashes with the Islamic State group, also known as ISIS.

However, ISIS mounted heavy resistance, sending car bombs to thwart their advances, Reuters reported. Shiite and government fighters were in control of the city's eastern, southern and western approaches, though it might be some time before they attempt to enter the city itself, according to Iraq officials, the Washington Post reported.

ISIS has been building up its defenses in Fallujah since gaining control several months ago, planting mines to repel government forces. Tribal and insurgent sources told Reuters that ISIS had staged attacks early Friday in villages between Fallujah and Ramadi – a move possibly meant to head off a coordinated between the two cities, both of which have become frontlines in the battle against ISIS in Iraq.

Iraqi authorities vowed to retake Ramadi, capital of Anbar province, after it fell to ISIS two months ago, but recently shifted to Fallujah in light of its more strategic positioning and proximity to Baghdad, Reuters reported. "We can’t go to Ramadi first and leave our back exposed. This is why Fallujah is a prior target," said Muen al-Kadhimi, a senior aide to a Shiite militia leader. U.S. officials apparently signed off on the plan to hold off on retaking Ramadi after criticizing the Iraqi military's inability to defend the city.

Both the U.S. and Iraq government are wary of giving more of a role to the Shiite militias, which are supported by Iran. Their advance has reportedly set off alarm among the largely Sunni population in Fallujah, where about 50,000 civilians remain. Shiite militias have been accused of sectarian violence, looting and burning Sunni homes and targeting Sunni civilians.

ISIS’ success in Anbar has dealt a major blow to Iraqi Prime Minister Haider al-Abadi’s image, as Baghdad’s military continues to lose territory to the group despite having vowed to wage a strong counteroffensive. U.S.-led coalition strikes in Fallujah have reportedly set back ISIS, but have also been responsible for civilian casualties. In the immediate aftermath of Ramadi’s fall, Abadi vowed that the city could be retaken in only a few days. Months on, both Fallujah and Ramadi remained in ISIS hands, as Shiite militia groups were reportedly leading the fight.