— Thousands of desperate Iraqi Yazidis who have been trapped by Islamist extremists on a parched mountaintop for almost a week trekked Friday into Syrian territory, seeking refuge in another war-ravaged country.

Some managed to collect water and food that had been dropped overnight by U.S. planes before heading northwest on a 12-mile walk across mountains and desert to the Syrian border. There, Syrian Kurdish forces waited to transport them to refugee camps or to safe crossings back into the Kurdish region of Iraq.

Mount Sinjar had become a prison for as many as 40,000 civilians who fled to its barren peaks to escape Islamic State fighters who seized the surrounding area last weekend. The Yazidis’ plight — and warnings that children and the elderly were dying — caused international outrage and prompted Washington to conduct humanitarian airdrops for the stranded Yazidis and airstrikes against the militants, to prevent what President Obama described as an attempted genocide.

The followers of the ancient Yazidi religion are particularly vulnerable to the Islamic State extremists, who consider the sect’s members apostates and have vowed to exterminate them.

Kurdish forces from Iraq, Syria and Turkey organized the evacuations and were positioned along the escape route to protect refugees from the extremists. The organizers said Friday that around 20,000 people had been rescued from the area but most from hideouts in the vicinity of Mount Sinjar, rather than on the mountain.

Trapped on Sinjar Mountain

As few as 10 percent of those on the mountain have managed to leave, said Serbast Babili, the commander with Iraqi Kurdish forces overseeing the operation. He spoke from the battlefield near the Sinjar village of Sinoon, where, he said, his troops were fending off Islamic State attempts to disrupt the evacuation.

Saleh Mehdi Abbas, 31, said his family was one of around 300 trekking toward the Syrian border Friday. He had left his area of the mountain at 3 a.m., he said, then walked for about an hour to pick up food and water in an area where U.S. planes made food drops overnight, before moving on.

“We are all marching,” he said in a telephone interview. “Now we are in the desert and near the Syrian border. We just hope that there are vehicles there to pick us up. We can’t go much longer.”

The isolated terrain, and the fact that the only possible escape route traverses Syrian territory, has limited the involvement of international humanitarian organizations in the rescue effort. A United Nations spokesman said he could not confirm that an evacuation was taking place, although he said the agency had reports of “movement.”

However, the International Rescue Committee (IRC) said Friday that it was providing emergency medical care for up to 4,000 dehydrated Yazidis who had arrived in a refugee camp in Syria’s Hasakah province a day earlier. The Kurdish area of Syria is relatively secure, though Kurdish forces have been battling off Islamic State attacks in the area for more than a year.

The refugees were suffering from dehydration, sunstroke and diarrhea, and some were in need of urgent treatment for war injuries, the aid organization said.

Iraqi Kurdish forces are repelling Islamic State advances on the southern side of the mountain, while the evacuation route on the mountain’s northern side is being organized by the fighters from the Kurdistan Workers’ Party and its Syrian spinoff, the Popular Protection Units, or YPG. The workers’ party is better known by its Kurdish acronym PKK, and it is designated a terrorist group by the United States.

As fighting intensifies in north Iraq, the country's minorities, including Christians, have been forced to flee their homes and move into the Kurdish-controlled regions of the country. Displaced Christians spoke to the United Nations High Commissioner for Refugees Thursday -- the same day that President Obama authorized targeted airstrikes in Iraq against Islamic State militants. (United Nations High Commissioner for Refugees (UNHCR))

“Most of them walk on foot to the border,” said Redur Xelil, a spokesman for the YPG. “We are still trying to reach many people in the mountain. It’s a large area.”

There were conflicting reports about whether the Kurdish forces coordinating the evacuation were allowing men of fighting age to leave the mountain. Ziad Qasim, 27, whose family was about a mile from the start of the evacuation route, said he had been told by a militiaman that whoever could carry weapons had to stay to fight.

“My wife and my father say they won’t leave without me,” he said by telephone. “What are we going to do?”

The IRC said most of those it was treating were women and children.

Majid Shingali, a Sinjar parliamentarian involved in the evacuations, said that one man was being allowed to escort every family out of the mountains but that any other male relatives should stay to fight. Local Yazidis have set up their own armed group that is coordinating with the Kurdish forces.

Shingali and Babili said the Iraqi air force had airlifted at least 60 of those too sick to walk off the mountainside Thursday night. The Iraqi government did not respond to requests for comment.

“It looks like in the next 24 hours we may have the whole north side of the mountain cleared,” Shingali said, adding that the Kurdish forces were opening a route to Syria that is accessible by vehicle.

But those stranded on the south side of the mountain — who would have to traverse its peak to escape and where the terrain is less conducive to airdrops — remained desperate for supplies.

When contacted by phone Friday morning, Shihab Balki, 23, had left the mountain to sneak into a nearby village to search for water. The village has been deserted since Islamic State forces swept through Sunday.

“I had to take a risk,” he said. “We received nothing today. I heard the sounds of planes in the night, but we couldn’t see anything.”

Mustafa Salim in Baghdad contributed to this report.