MOSUL, Iraq — Iraqi and U.S. commanders offered conflicting accounts Thursday of progress in western Mosul, where U.S.-backed Iraqi forces have been battling the Islamic State group for nearly a month as they try to retake the remainder of the city.

Maj. Gen. Joseph Martin, the American commander of coalition ground forces in Iraq, said the troops had recaptured "a little over a third" of neighborhoods west of the Tigris River, while Brig. Gen. Yahya Rasool, an Iraqi military spokesman, said they had retaken up to 60 percent, with fighting still underway. Iraq declared eastern Mosul "fully liberated" in January.

Iraqi officials have overstated gains in the past, declaring areas liberated from ISIS militants only to see the resumption of fighting or militant attacks. The extremists have targeted eastern Mosul with bombings and other attacks on several occasions in recent weeks.

Front-line commanders meanwhile said progress has been slow over the past week, with troops advancing just a few hundred meters (yards) in the face of ISIS car bomb attacks.

Lt. Ahmed Mahmoud of the militarized Federal Police said his unit was waiting until special forces cleared nearby neighborhoods before moving in to hold the territory. He spoke near Mosul's antiquities museum, which Iraqi forces recaptured earlier this month.

He said Iraqi forces had launched three coordinated thrusts in western Mosul, hoping to overwhelm ISIS defenses.

The militants captured Mosul, Iraq's second largest city, when they swept across the country's north in the summer of 2014. Iraqi forces have gradually clawed back territory since then, and launched a massive operation to retake Mosul in October.

Despite U.S. air support, the Iraqi advance has been slowed by snipers, roadside explosives, and suicide car and truck bombs.

A suicide attacker driving a bulldozer rigged with explosives plowed through the Federal Police's front line on Wednesday, killing more than 10 soldiers and wounding several others, according to a Federal Police medic who spoke on condition of anonymity in line with regulations. Iraq's military does not release casualty figures.