BARTELLA, Iraq — U.S.-backed Iraqi forces fought their way inside two villages Monday as they crept closer to Mosul a week into an offensive to retake the Islamic State-held city, but they also faced questions over a suspected airstrike on a mosque that killed 13 people.

Iraqi special forces shelled militant positions before dawn near Bartella, a historically Christian town east of Mosul that they had retaken last week. With patriotic music blaring from loudspeakers on their Humvees, they then pushed into the village of Tob Zawa, about 51/2 miles from Mosul, amid heavy clashes.

Until now, most of the fighting has been in largely uninhabited towns and villages, but the special forces found more than 70 civilians sheltering in Tob Zawa. They will encounter many more civilians as they get closer to Mosul, still home to more than 1 million people.

The Iraqi Federal Police, a military-style force, pushed into a second village in the Shura district south of Mosul, where they fired a large anti-aircraft gun and rocket-propelled grenades. They later appeared to have secured the village, a cluster of squat homes on a desert plain, and handed out water and other aid to civilians.

The U.S.-led coalition said it carried out six airstrikes Sunday near Mosul, destroying 19 fighting positions and 17 vehicles, as well as rocket and mortar launchers, artillery and tunnels.

Human Rights Watch called for an investigation into last week's purported airstrike in northern Iraq that hit the women's section of a Shiite mosque in the town of Daquq.

The strike happened amid a large Islamic State assault on Kirkuk that appeared aimed at diverting attention from Mosul, Iraq's second-largest city.

The Islamic State attack on Kirkuk, 100 miles southeast of Mosul, lasted for two days and killed at least 80 people, mainly members of the Kurdish security forces that took control of the city in 2014 as Iraqi forces crumbled amid an Islamic State advance.

Human Rights Watch said Daquq's residents believe Friday's attack was an airstrike because of the extent of the destruction and because planes could be heard overhead. The New York-based group said at least 13 people were reported killed.

The coalition and the Iraqi military, which are waging the offensive, are the only parties known to be flying military aircraft.

Col. John Dorrian, a U.S. military spokesman, said the coalition had “definitively determined” it did not conduct the airstrike that killed civilians in Daquq and had shared its findings with the Iraqi government, which is doing its own investigation.

“The Coalition uses precision munitions and an exhaustive process to reduce the possibility of civilian casualties and collateral damage because the preservation of civilian life is (of) paramount importance to us,” Dorrian said.

Iraqi Brig. Gen. Yahya Rasool, spokesman for the Joint Military Command, confirmed the Iraqi government was investigating the attack. He declined to say whether Iraqi or coalition planes were in the area at the time.