Story highlights Thousands of minority Yazidis have fled from ISIS into remote Iraqi mountains

Islamic militants told them to convert to Islam, be imprisoned or die

One Yazidi recalls fleeing ISIS in the heat of summer, without food or drink

"I saw dogs feeding off dead bodies," he recalls

People of the Yazidi faith in northern Iraq face an impossible choice: Stay and risk being killed by Islamist insurgents, or flee across the barren desert, facing starvation and thirst.

Its hard to imagine the suffering that minority Yazidis have endured in recent weeks as they've fled from ISIS militants into remote, rugged, sparse mountains.

"With my own eyes, I saw dogs feeding off dead bodies," one of those Yazidis, a man named Tariq, told CNN.

"It's not a crisis. It's a catastrophe."

Descendants of Kurds and followers of an ancient pre-Islamic religion, Yazidis are small in number with a big sense of community.

Now some of them are under siege or under fire, targeted by ISIS for not succumbing to demands to convert to Islam or else. Others, like Tariq, have managed to find some refuge in recent days, though worries remain about finding the resources they need to survive.

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Wherever they are, whatever they are doing, Yazidis don't feel safe or secure or free.

They certainly aren't home.

'We had nothing'

The 33-year-old Tariq's nightmare began in his home village of Tal Benat-Sinjar at 9 a.m. on August 3. That's when he and others started receiving calls from neighboring villages, telling them "Daish," the Arabic term for ISIS, was on their doorsteps.

The choices were simple: Stay, convert to Islam, and become one with ISIS. Stay and risk death or imprisonment, as Tariq said he knew happened to a family of one man, three women and four children. Or run away, in hopes of finding some place they could live safely or, at least, freely away from ISIS' grasp.

More than 300 Yazidi families -- Tariq among them -- picked the third option.

Their first refuge was the abandoned ruins of a tiny, old village that had been previously used for herding cattle and sheep and was next to a cement factory.

An ISIS messenger caught up with them there to deliver an ultimatum: Convert by noon the next day or die.

Tariq and his neighbors fled again, this time up Mount Sinjar. They followed a zig-zagging road five kilometers (three miles) up to the mountain's desolate top.

The hundreds of Yazidis, including many elderly and children, had each other. But not much else, having escaped with little more than the clothes on their backs and the bread in their hands.

ISIS militants choked off any chance of restocking by surrounding the roads leading up to the mountain.

"At one point, 15 people shared 1.5 gallons of water," Tariq recalled. "We had nothing."

People drop to ground of hunger

If ISIS fighters didn't kill the Yazidis, their siege did.

Tariq's 80-year-old father was among the dead, dying two days after being stranded on the mountaintop in the extreme heat without anything to eat or drink.

He wasn't alone. Tariq said he counted between 500 and 1,000 bodies, some of which went from cherished loved ones one moment to food for hungry dogs the next.

"I saw people dropping on the ground from being so tired on their empty stomachs," he told CNN.

Tariq, at least, is alive. Fighters with the Kurdistan Workers Party -- or PKK, which the U.S. State Department labels a terrorist group though they now share a common enemy in ISIS -- were able to break the siege so that he and other Yazidis could safely escape.

The subsequent journey took them through parts of northern Iraq, across the border into Syria, then eventually back to Iraq. Their last stop -- for now -- is a village in Dhok province that Tariq characterized as being "in the middle of nowhere."

Still, even if he's safe for now, the danger hasn't gone away.

First off, ISIS hasn't backed off. The U.S. military noted Saturday that the militants "indiscriminately attacked" Yazidis near the SInjar Mountains, prompting American airstrikes.

Attacks aren't the only reasons Yazidis' lives are at risk. Thousands of them don't have the food or water they need, especially in Iraq's scorching summer.

"There are more than 20,000 families still stranded on the mountain in more remote areas," Tariq said.

"If no one gets them food or water in time, they will face death."