Displaced families from the minority Yazidi sect fled the violence in the Iraqi town of Sinjar, just west of Mosul, and took refuge at Dohuk province on Aug. 4. (Ari Jala/Reuters)

Politicians appealed Wednesday for emergency aid for thousands of minority Iraqis who have been stranded with little food on a mountaintop in the country’s northwest, surrounded by al-Qaeda-inspired rebels.

For nearly two months, Kurdish forces had managed to protect the area from the Sunni extremists who have rampaged through much of northern Iraq, slaughtering opponents, destroying ancient shrines and demanding that people of other religions convert or die. But last weekend the famously tough Kurdish fighters suffered their first setbacks in the Sinjar region, prompting hundreds of thousands of civilians to flee.

An estimated 10,000 to 40,000 of them sought refuge on the craggy peaks of Mount Sinjar — largely members of the minority Yazidi sect. They fear death if they descend into areas controlled by the extremist rebels, who consider them apostates. Kurdish forces have so far failed to break through the militants’ lines to reach them, despite launching a counteroffensive early this week.

The Iraqi government conducted two airdrops of aid to the desperate refugees on Wednesday, but humanitarian workers said they did not come close to meeting the growing need. Some of the water bottles in the aid bundles cracked open.

“Is help coming?” one of those trapped on the mountain, 23-year-old Shihab Balki, asked when contacted by cellphone — one of the few belonging to the refugees that still had battery life. He said that at least 17 children have died on the mountain because of the inhospitable conditions.

Iraqi politician Vian Dakhil makes a raw, emotional plea for the protection of the Yazidi people before Iraqi parliament. (YouTube/Al Sumaria TV)

“I’m standing here next to an old lady and a child lying on the ground. They are not dead, but we fear they are dying,” Balki said.

UNICEF says it has confirmed that children have perished on Mount Sinjar but does not have verified up-to-date figures.

Balki said later Wednesday that he had managed to secure about four gallons of water for his family of seven from one of the day’s airdrops — not nearly enough in the hot Iraqi summer. Many of the bottles dropped in a wooden crate had cracked, their precious contents spilling onto the rocks, he said. Earlier airdrops included food and milk, but the cartons of milk also smashed on the mountainside, he said.

Haji Ghandour, a Yazidi member of parliament in Baghdad, said the shortage of aid was acute.

“There are some airdrops, but they aren’t even covering half the need,” he said. “Most of these supplies fall near to [Islamic State fighters], others break and are ruined. The operation is not accurate.”

The United Nations says the Iraqi government has yet to take up an offer of technical assistance for airdrops, which are being coordinated with local authorities in the semiautonomous Kurdish region in northeastern Iraq.

Falah Mustafa Bakir, the Kurdistan region’s foreign minister, argued that Iraq simply lacks the capacity to provide aid and needs international help. “This is not a time for technical assistance,” he said. “This is a time for immediate action. Children are dying.”

Displaced families from the minority Yazidi sect take refuge Aug. 4 in Dohuk province. Prime Minister Nouri al-Maliki has ordered his air force to back Kurdish forces against Islamic State fighters. (Ari Jala/Reuters)

In Washington, Obama administration officials did not respond Wednesday to queries about whether the U.S. government was considering providing assistance.

Trouble on several fronts

Meanwhile, tens of thousands of newly displaced people have flooded into the Kurdish region, which Bakir said lacks the finances to assist them. The region, which is home to just over 5 million residents, is now hosting an additional 1.5 million people — refugees from the Syrian war and internally displaced Iraqis, he said.

Kurdish officials had warned for weeks that they were unable to maintain the fight along the semiautonomous region’s 650-mile-long front with the militants, unless the Kurds got outside support. A lack of ammunition and advanced weaponry forced the retreat from Sinjar, Kurdish officials say.

The Kurds say they are trying to put out fires on multiple fronts, trying to recapture land only to be attacked elsewhere as the Islamic State continues to jab at its boundaries.

That threat was underscored on Wednesday when, as Kurdish forces continued their counter­offensive near Sinjar, they were forced to send reinforcements 150 miles east to Makhmur and Gweir as militants attempted to push closer to their regional capital, Irbil.

“It’s not fair that we are left fighting these terrorists alone,” said Bakir, the Kurdistan region’s foreign minister. “We need immediate action. We look to the United States, we look to NATO.”

“The West have armed many groups around the world. Why not help us be in the front against terrorism?” Bakir said. “We don’t understand.”

Kurds receive air cover

The Kurds are supposed to receive a share of weapons and budgetary outlays from the national government in Baghdad. But relations between the two governments have soured, as some prominent Kurdish leaders have called for independence.

In recent days, however, the Iraqi military has started providing air cover to Kurdish security forces known as pesh merga.

Still, Kurdish troops have not been paid for months because of the suspension of budget payments from Baghdad, and the northern region has struggled to procure military supplies. Those relations are likely to worsen if Iraqi Prime Minister Nouri al-Maliki stays in power, with a change in leadership seen by many as the only way of keeping the north from splitting away. Maliki has held the country’s top political job since 2006.

Maliki appeared defiant on Wednesday, even though the country’s religious authorities and his own party are indicating he should step aside. He argued that his political bloc had won the largest share in the elections in April and should be allowed to nominate the prime minister.

If the constitution is ignored, it will “open the gates of hell” in Iraq, he said.

Mustafa Salim in Baghdad and Karen DeYoung in Washington contributed to this report.