With more than half of the 40,000 trapped Yazidis safely evacuated from Mount Sinjar, U.S. officials are working to rescue the remaining half who continue to suffer from thirst and hunger and are still at risk of being captured or killed.

U.S. Deputy National Security Adviser Ben Rhodes told Reuters on Sunday that the government is still considering alternatives for the safe evacuation of the remaining civilians on the mountain.

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The U.S. is coordinating with the Kurdish forces, the United Nations and other allies to come up with the best strategy to bring the civilians to a safe place.

According to The Guardian, some 20,000 refugees - aided by the YPG, a Kurdish rebel group in Syria - had escaped Mount Sinjar on Sunday night.

Some of the refugees claimed the escape was made possible when a U.S. air strike had forced Islamic State (IS) militants to withdraw their positions for around six hours.

The civilians had trekked for nearly 24 hours crossing over a mountain range into Syria and were then escorted back to Iraqi Kurdistan by the Kurdish forces.

Barakat Issa, a refugee who had arrived in Iraqi Kurdistan on Saturday, called the day-long journey impossible.

"There was a three-year-old child with me that had to walk eight hours non-stop in very rough terrain," he said.

While Sunday's evacuation had been successful, thousands more are believed trapped in the southern area of the 60-mile-long ridge.

Barakat said the main concern for the trapped Yazidis was the lack of water, saying that many had already died of thirst because there was little water to be found in the mountain.

He added that the people in the mountains were having a hard time accessing the aid. Barakat said the packages were being dropped on a peak deep in the mountains. He estimated that less than 10 percent of the people were able to gain access to the aid.

Others claimed the food and water packets broke when it hit the ground.

Another refugee Ghassan Salim, 40, called the situation a "human catastrophe." He said the children in the mountain needed to be rescued and noted that other minorities like the Christians and Shabbak needed help as well.

Barakat claimed that IS rebels had seized two other Yazidi villages. The villagers were given an ultimatum to either convert to Islam or face death, he said.

Meanwhile, Kurdish forces said they had regained control of three villages southwest of Erbil on Sunday. They urged Washington to continue the air strikes on the IS to keep the momentum rolling.

Iraqi Kurdistan President Masoud Barzani called on the international community on Sunday to provide Kurds weapons to boost their offense against the IS.

TagsYazidi, religious minority, YPG, Iraq, Mount Sinjar, Masoud Barzani, Kurdistan