A mass evacuation of Yazidis hiding from extremist fighters on Iraq's Sinjar Mountains is unlikely following an assessment by the U.S. State Department and military that found far fewer people trapped than previously feared.

Once believed to be in the tens of thousands, the number of Yazidis in the mountains is "now in the low thousands," Brett McGurk, a deputy assistant secretary of state, told CNN on Wednesday.

The news broke the same day a senior commander with the Islamic State, formerly known as the Islamic State in Iraq and Syria, claimed ISIS fighters abducted more than 100 Yazidi women and children from Sinjar.

The ISIS commander, who has knowledge of the events that unfolded, said the fighters killed a large number of men when they took over the town more than a week ago.

"At that time, they took Yazidi women and children, and I can confirm those women and children have entered Mosul," the commander said by telephone. "...The Islamic State is taking this opportunity to call them to Islam."

While CNN cannot independently confirm the claim, it follows reports by survivors who describe ISIS fighters grabbing families and separating the men from the women and children.

The plight of the Yazidis, coupled with the ISIS assault against Iraq's semiautonomous Kurdish region, prompted the United States to begin targeted airstrikes over the past several days.

The aim, according to President Barack Obama, is to help protect U.S. personnel in the area and to destroy ISIS positions around the mountains to ease the threat to minority groups.

The United States deployed 129 military advisers to get a firsthand look at the humanitarian crisis unfolding as ISIS fighters threaten Iraq's ethnic and religious minorities: Yazidis, Christians and Kurds.

As part of that effort, a group of about 20 U.S. State Department and military personnel spent 24 hours in the mountains to assess the numbers and conditions, Pentagon spokesman Rear Adm. John Kirby said.

"The Yazidis who remain are in better condition than previously believed and continue to have access to the food and water that we have dropped," he said, citing the success of humanitarian airdrops and airstrikes against ISIS.

The problem, though, is far from over.

The United Nations on Wednesday announced its highest level of emergency for a humanitarian crisis, saying the number of people on the run from ISIS is of grave concern.

It estimates more than 400,000 people have been driven from their homes since June, when ISIS swept across the border from Syria into Iraq.

The group has waged a brutal campaign while seizing large swaths of northern and western Iraq, aiming to establish a caliphate -- an Islamic state -- that stretches from Syria to Iraq.

Of those displaced, more than 200,000 have poured into Dohuk province in recent weeks, where refugee camps have swelled since ISIS began its assault against Yazidis, Christians and Kurds.

By declaring what it calls a "Level 3 Emergency," the United Nations says it will trigger more resources to help.

Obama this week ordered the military advisers to the Kurdish capital of Irbil to assess the humanitarian crisis.

The advisers, made up of Marines and special operations forces, join hundreds of other American advisers already in the country advising Iraqi troops in their fight against ISIS, an offshoot of al Qaeda in Iraq.

The group has waged a brutal campaign while seizing large areas of territory this year in Iraq, aiming to establish a caliphate.

Adding to the crisis is Prime Minister Nuri al-Maliki's refusal to step down after Haider al-Abadi was nominated to replace him.

In a televised address on Wednesday, he called the move to appoint al-Abadi as prime minister a constitutional violation.

Al-Maliki's political party won a majority during parliamentary elections in April, but not a super majority. Even so, al-Maliki has maintained that because his party won a majority, the next Prime Minister should come from his party.

He has filed a lawsuit in federal court to stop the formation of a new government, and he has said he wouldn't step down until the court has ruled.

"We need to protect the federal court and its decisions; no one has any ground to go against this court," al-Maliki said, while not specifically mentioning the name of Prime Minister-designate al-Abadi or any other leaders.

(CNN)