The U.S. began targeting fighters from the Islamic State with airstrikes Aug. 8, allowing Kurdish forces to fend off an advance on their regional capital of Irbil and to help tens of thousands of members of religious minorities escape the extremists' onslaught.
Recapturing the entire Mosul Dam and the territory surrounding its reservoir would be a significant victory against the Islamic State group, which has seized swaths of northern and western Iraq and northeastern Syria. The dam on the Tigris supplies electricity and water to a large part of the country.
The Kurdish forces, known as peshmerga, launched the operation early Sunday to retake the Mosul Dam, said Gen. Tawfik Desty, a Kurdish commander, after a day of U.S. and Iraqi airstrikes pushed back Islamic State fighters.
A spokesman for the peshmerga said the clashes were moving eastward.
"The west is in control of peshmerga. But there are some battles taking place in the (east) right now," said Halgurd Hekmat, peshmerga spokesman.
Another commander confirmed the information, saying that by Sunday evening, peshmerga forces had crossed the Tigris to the broad plains held by the Islamic State.
The U.S. military conducted 14 airstrikes Sunday, damaging or destroying 10 armed vehicles, seven Humvees, two armored personnel carriers and one checkpoint, according to a statement by the Central Command. On Saturday, it carried out nine airstrikes near the dam, destroying four armored personnel carriers, seven armed vehicles, two Humvees and another armored vehicle, the command said.
The peshmerga, the fighting force of the largely autonomous Kurdish region of northern Iraq, surrounded the Islamic State-held city of Tel Kayf after taking the nearby town of Tel Kasouf, said the commander, who spoke on condition of anonymity in line with military regulations.
The advance of Kurdish forces was hindered by roadside bombs and buildings rigged with explosives, planted by retreating Islamic State fighters, he said.
"They have reached inside the dam. There is no fighting, just the (roadside) bombs, and the abandoned buildings are all rigged with explosives," he said. "We will continue to advance and advance until we are given further instruction."
The commander said the evening advance occurred after the Iraqi government delivered 16 military Humvees, at least one with a mechanized bomb-disposal unit that was dismantling the roadside explosives.
Even as they advanced around the dam in northern Iraq, the commander said fighting forces were so poorly armed that he did not believe they could hold onto captured territory without a fast infusion of weapons — or continued U.S. airstrikes.
"We don't have the right weapons," he said.
Troubled relations between the Kurds and the central government in Baghdad have hindered the supply of arms to the force, leaving them overstretched and outgunned as the Islamic State group advanced.
Earlier this month, the militants swooped into Kurdish-held territory, seizing a border crossing and the Mosul dam. They also took control of villages around a northern mountain chain dominated by the Yazidis — adherents of an ancient faith seen as heretical by the militants.
The militants also took over villages near Irbil inhabited by Christians, and two Kurdish towns, Makhmour and Gweir.
Those seizures led to the flight of tens of thousands of Yazidis, Christians and Kurds into safer, Kurdish-held areas, and threatened to march onto Irbil itself.
Their advance was halted by U.S. airstrikes, the first American military involvement in Iraq since its troops pulled out in 2011. U.S. officials also said they would begin supplying weapons to Kurdish forces and said they had already been giving them some automatic rifles and ammunition.
But peshmerga forces say they haven't yet received any new supplies, and it's not clear how long the U.S. airstrikes will continue.
The senior commander said officers of his rank were told the U.S. had delivered mounted machine guns and rocket-propelled grenades to the Kurdish Defense Ministry, but they had not been distributed.
He said the weapons, while powerful, could not stop the advance of the Islamic State group, which has used heavily armored U.S. Humvees taken from Iraqi troops who abandoned them in June when the militants first swept through the territory.
Echoing a complaint by other commanders, he said the peshmerga lacked the firepower to pierce Humvee armor, adding that they needed to be closer than 330 feet (100 meters) from the vehicle with an RPG in order to destroy it. He said the weapons mounted on Humvees typically allowed militants to stay back 1,300 feet (400 meters).