(CNN) Iraqi paramilitary forces are in a raging battle to take a key ISIS stronghold west of Mosul, but their presence is prompting fears that the fighting could result in the escalation of sectarian violence in Iraq.

The Shia-led Popular Mobilization Units, or PMUs, have significantly advanced against ISIS in the Tal Afar area, with the help of the Iraqi air force targeting the terror group and killing 12 militants, according to Iraq's Joint Operations Command.

Tal Afar is a predominantly Sunni city that was divided between Sunni and Shia Turkmens before ISIS captured it in 2014.

For a month, an Iraqi-led coalition has waged a military operation to retake Mosul, Iraq's second-most populous city and ISIS' last major stronghold in the country.

'This means another civil war'

. Tal Afar is about 70 kilometers (43 miles) west of Mosul. The PMU released a statement Friday saying their forces are surrounding the town from the west and the south. Three days ago, paramilitary forces took the strategically important Tal Afar air base , which can serve as a launching point in the battle with ISIS west of MosulTal Afar is about 70 kilometers (43 miles) west of Mosul.

Izzeddin Aldola, a member of the Iraqi parliament who represent Sunnis from the Tal Afar area, told CNN by phone of fears about PMU forces entering the city.

"Iraqi Prime Minister Haider al-Abadi promised us that only the Iraqi army will enter Tal Afar," Aldola said. "We are very worried, and even if only people from Tal Afar fight ISIS in the city, this means another civil war."

On Friday, Hadi al-Amiri, the head of the Iranian-backed Badr Organization and a PMU commander, said in a video released by the group: "We will let the sons of Tal Afar liberate Tal Afar, and if they need our help, then we are ready."

Those fighting for Tal Afar, Amiri continued, will be citizens of that city. An Iraqi military brigade will fight alongside the Hashd al Shabi, another name for PMU -- which includes a Shia paramilitary group called Sons of Tal Afar, a Sunni Hashd paramilitary also from Tal Afar, and members of the federal police.

The Amiri statement appears to leave the door open to Shia paramilitaries entering into the battle for Tal Afar.

Tension between Baghdad government, Kurds

Further complicating the Mosul offensive, the Iraqi Prime Minister has maintained that Kurdish forces must withdraw from towns captured from ISIS once the terror group has been defeated. Tensions are mounting between Baghdad and the Kurdistan Regional Government over future control of the territory in northern Iraq.

Kurdish fighters, known as Peshmerga, are playing a critical role in the battle to defeat the terror group, fighting alongside Iraqi government troops and other forces in the coalition to retake Mosul, the capital of Nineveh province.

But cracks are emerging in the anti-ISIS partnership over the question of what the semiautonomous Kurdish Regional Government plans for areas it captures from the terror group.

Kurdish President Massoud Barzani and Abadi have released statements in recent days that underline their conflicting positions.

Barzani said he wouldn't permit residents who had supported ISIS to return to liberated villages, signaling Sunni Arabs may not be welcome.

"We have shed a lot of precious blood to liberate areas from (ISIS)," he said at a press conference Wednesday.

A report this week from Human Rights Watch also accused the Kurds of unlawfully targeting and destroying Arab homes in regions they have retaken from ISIS.

Kurdish officials strongly denied any systematic destruction of Arab-owned homes, and Barzani dismissed the report as "unfair."

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In July, Barzani told Human Rights Watch the Kurdish Regional Government would not allow Sunni Arabs to return to villages that Saddam Hussein had "Arabized." In his view, those are historically Kurdish lands needed for a potential future independent Kurdistan, which Barzani has long championed.

Abadi has reiterated that the agreement under which Iraqi federal forces and Peshmerga were cooperating in Nineveh province stated that the Kurds must return to their previous positions after the battle was won.

Numerous disputed territories in Iraq are nominally under Baghdad's jurisdiction but controlled and claimed by the Kurdistan Regional Government.

Editor's note: A previous version of the story incorrectly identified the Shia paramilitary group Sons of Tal Afar as the sole group fighting to liberate the city, in a quote attributed to Hadi al-Amiri.