DOHUK, Iraq--Thousands of Yazidi refugees stranded for more than a week in barren Iraqi mountains need more aid, even though U.S. airstrikes and airdrops appear to have improved the conditions there, according to officials and some families who have escaped.

The U.S. on Wednesday dispatched a small assessment team that spent 24 hours on the Sinjar Mountains and concluded that a large number of the trapped members of Iraq's Yazidi religious minority had already managed to flee. The assessment makes it unlikely the U.S. military will carry out a risky evacuation, which had been considered, from the mountains that are besieged on one side by Islamist militants, said U.S. officials.

For the past week, officials from Iraq, the U.S., andinternational aid agencies have offered different estimates on the number of Yazidis on the mountains, and struggled to keep track of how many were successfully fleeing each day across different routes.

Some 95,000 people have left Sinjar area since Aug. 6, said Ned Colt, a spokesman for the UN Refugee Agency in Iraq. Some have fled from the mountain or crossed through it from other parts of the vast Sinjar plain in northern Iraq, Mr. Colt said. At least 15,000 of those are living in a camp across the border in Syria and 80,000 have crossed into Dohuk in the Kurdish region of Iraq. The update suggested that far more people had been on the Sinjar mountains than initially thought, with the U.N. last week giving a rough estimate of 40,000.

But it is still not clear how many are still there, and why. The U.S. assessment on Wednesday that those left on the Sinjar mountains could flee, and that an evacuation wasn't necessary, appeared to surprise local Iraqi officials and disappoint some Yazidis who have relatives still on the mountains.

"How much can a small team of people see in a mountain that is 64 kilometers wide? There are valleys and caves where people are living," said Shawkat Othman, a director for Dohuk city authority, in the northern province of Dohuk where thousands of displaced Iraqis have sought refuge from an offensive by the militant group calling itself Islamic State. "I am sure they didn't see 10% of Sinjar," Mr. Othman said, referring to the U.S. assessment team.

Zuhair Lazgeen, a Yazidi activist living in Dohuk who has relatives on Sinjar, said it wasn't clear how many people were still left on the mountainside but that the number was in the thousands. Their conditions appear to have improved, he said, except for the elderly or sick. "Elderly people who can't or prefer not to walk cannot leave," Mr. Lazgeen said. "My relatives are starting to say, you can smell the dead people. Everywhere you go."

The Yazidis have been escaping their mountain hide-outs in different ways and routes--some fleeing along the base of the mountain, others going across the border through to Syria with the help of a Kurdish militia, or more recently, being plucked to safety in Iraqi helicopter rescue missions. The fluid situation and the ruggedness of the mountainside have made it difficult to see or assess the number of refugees and have posed challenges for policy makers.

Mr. Colt of the UN Refugee Agency said it has been a real challenge to estimate any numbers because the agency doesn't have its own people in the areas affected and can only register the refugees crossing out into Dohuk. He said there was anecdotal evidence from those still crossing out into Dohuk on Thursday that the route was now safe, and that some families are returning to either pick up relatives en route or belongings they need.

In the Kurdish border town of Zakho, now home to thousands of displaced Yazidis, many refugees disagreed with Washington's assessment that the members of their community could leave Mount Sinjar.

Others, who recently arrived at the Dalal Park, a public space now housing some 1,500 Yazidis in Zakho said the route off the mountain has been secured by the Syrian Kurdish militia called the People's Protection Units, or YPG, but that many refugees were still too afraid to leave.

"The YPG are controlling it and ferrying people out on trucks, focusing on the most vulnerable," said Marwan Sabri, aged 34, who said he walked down from the mountain with 11 of his family. But Mr. Sabri said there is no food on the route, and added he saw "only two helicopters carrying emergency aid."

Hero Mirza, a 40-year-old market stall owner said that thousands on the mountain were trapped or too weak to leave. Mr. Mirza said he arrived in Zakho on Thursday carrying his 90-year-old mother.

Across Zakho, the Yazidi refugees are taking shelter in parks and abandoned buildings, or pitching tents on traffic circle. The Dohuk municipality official said the broader province now hosted nearly a million displaced Iraqis.

"The corridors to walk across the Islamic State lines are shifting and it is very dangerous," Mr. Mirza said. "Many are too scared or too weak."

Write to Nour Malas at nour.malas@wsj.com and Joe Parkinson at joe.parkinson@wsj.com

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(END) Dow Jones Newswires

August 14, 2014 12:15 ET (16:15 GMT)

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