Story highlights Kurdish council says Peshmerga takes town of Sinjar, nearby villages

Morale is high, ISIS fighters are fleeing toward strongholds, council adds

This push comes against ISIS is part of a recent, coalition push in northern Iraq

32 truckloads of food, water, other aid head to those on Iraq's Sinjar Mountain

Kurdish Peshmerga fighters claimed to take control Saturday of Sinjar, the northern Iraqi town that ISIS militants stormed this summer causing minority Yazidis to flee into nearby mountains and spawning a humanitarian crisis.

The Kurdistan Region Security Council (KRSC) said on Twitter that its forces entered Sinjar district around 1:45 p.m.(9:45 a.m. ET) and, just over an hour later, "succeeded in taking complete control of it & nearby villages." The message ended "#Shingal #Kurds." Shingal is another name for Sinjar.

The advance is the latest in recent days by Kurdish forces against ISIS, which has been blamed for atrocities around the area for its treatment of those by any who resist or don't subscribe to its extremist Islamist beliefs.

And few, if any, have gotten worse treatment than the Yazidis -- one of the world's smallest and oldest monotheistic religious minority groups. Yazidis, most of whom are ethnic Kurds, revere an angel figure that some Muslims believe to be the devil.

Last summer, ISIS slaughtered Yazidis by the hundreds , according to Vian Dakhil, the only lawmaker representing the Yazidis in Iraq's Parliament. Women in the group were "treated like cattle," Kurdish Regional Government adviser Nazand Begikhani said. Many were enslaved, raped and sold by ISIS.

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The town of Sinjar became central to this drama, when Yazidi residents ran for their lives to Sinjar Mountain, just to the north.

But they had very little food, medical care or water, shortages compounded by Iraq's intense summer heat.

Their dire situation, as well as the harsh treatment they got from ISIS simply due to their religious beliefs, spurred an international coalition to act.

This effort began with the airdrop of supplies to Sinjar Mountain. Rescues came next. And now, the U.S.-led coalition is waging regular airstrikes targeting ISIS in Iraq and neighboring Syria -- an air campaign that helped pave the way for the recapture of Sinjar.

Fight over Sinjar Mountain, surrounding area

This summer's combination of humanitarian and military efforts helped, as thousands of Yazidis fled on foot to Syria.

Still, a few hundred remained on Sinjar Mountain. And ISIS never really went away.

In fact, the tug-of-war in the region has continued for months -- prompting a fresh allied onslaught in recent days.

Tuesday night, coalition aircraft conducted 48 airstrikes near Sinjar -- the heaviest concentration of such airstrikes to date, according to two U.S. defense officials.

Masrour Barzani, chancellor of the KRSC, said Thursday this ground-and-air operation helped "open ... a corridor from south of Zummar to the Mountain Sinjar," giving direct access to those displaced on the mountain and in need of aid.

ISIS fighters, meanwhile, fled toward the Syrian border and ISIS strongholds such as Mosul and Tal Afar, the Kurdish agency said.

Kurdish agency: 'Morale remains high'

The Peshmerga are keeping up the heat.

A press release Saturday from the Kurdistan Region Security Council indicated these fighters launched a new phase of the offensive around 8 a.m. (midnight ET) south of Rabia to Sinjar Mountain.

Three hours later, the KRSC claimed its forces had taken "complete control of Mushrefa" but that they weren't done.

"The objective is to surround and clear an area of approximately 2,100 square kilometers (810 square miles)," the Kurdish agency said.

Meanwhile, humanitarian aid -- in the form of 32 truckloads of food, water and other needed aid -- began rolling out Saturday morning from Irbil, bound for Sinjar Mountain, the KRSC reported.

"Morale remains high as the Peshmerga continue to make advances on both fronts (north and south of Sinjar Mountain)," the Kurdish agency said.