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 town east of Mosul that they had retaken last week. They then pushed into the village of Tob Zawa, about 5 1/2 miles from Mosul, amid heavy clashes. The Iraqi Federal Police, a military-style force, pushed into a village in the district south of Mosul.