Kurdish fighters in northern Iraq are desperate for arms from Baghdad or even the U.S. to help fend off an onslaught from Islamic militants that may be aimed at creating a corridor for jihadist reinforcements from Turkey.

Despite U.S. air strikes aimed at fighters from Islamic State, the militant group formerly known as ISIS, Kurdish fighters known as Peshmerga say they remain under sustained attack on multiple fronts. Rumors of weapons and ammo en route from Baghdad and the U.S. are rife, yet a number of sources confirm they have not yet been seen.

“We hear about them, yes, but we don’t see them,” a Kurdish officer in Kirkuk told FoxNews.com. “They simply haven’t arrived.”

The Islamic State’s move on Kurdish territory, after weeks of threatening to expand its so-called caliphate into the south, has left many in the region puzzled. Islamic State initially said it planned to push South, towards the holy Shia sites of Karbala and Najaf, but a few days ago they turned suddenly North, ultimately triggering the U.S..response

“IS troops simply want to go everywhere - Paris, Washington, Cairo, London,” Rooz Bahjat, a senior Kurdish Intelligence officer, told FoxNews.com. “They want to take it all.”

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Bringing the Kurds into the fight, and putting a host of religious minorities in the crossfire, could prove costly to the Islamic State, Bahjat said.

“They made a grave error,” he said.

The U.S. air strikes have been effective, Bahjat said, but much more is needed. Islamic State forces are probing for weaknesses along an 800-mile battle front, and are still able to move freely around the arid landscape at will.

Some Kurdish intelligence sources suspect Islamic State’s motive in moving north was to open a path to northern Syria and Turkey, through which they could pull reinforcements. An estimated 1,500 fighters recently poured in from Syria, helping Islamic State control Iraq’s northwestern border.

Another theory for Islamic State’s push into Kurdish lands is that it sought to take advantage of the political wrangling in Baghdad, where Prime Minister Nouri al-Maliki has been forced from office but refuses to step down.

Kurdish officers are also at a loss to understand why the Iraqi army had not attacked from the south, which would have forced Islamic State to fight on two fronts.

“Maliki had the chance to shoot them in the back,” one officer complained, “but for some reason he won’t. We can’t explain this strange extraordinary action.”

With Islamic State heavily dug in in the western part of the country and in Mosul, attacks from the air are unlikely to dislodge the insurgents. And with a political or diplomatic solution nowhere in sight, Kurds are in “survival mode,” trying to accommodate the thousands of refugees stuck in the middle.

The best hope is that new Prime Minister Haider Al-Abadi can deliver an inclusive government which might undermine Sunni tribal support for Islamic State, effectively defeating it from within.

In the meantime Peshmerga forces remain outgunned, and not just at the front lines. Sources say that among the throngs of refugees fleeing north are hidden Islamic State members - disguised in preparation for an attack from within. Already there has been a rise in bombings throughout the region, and sleeper cells are feared to be in place.

But despite this the population of Kurdistan is more relaxed since US intervention. There was an initial period of panic as IS troops came within 30 miles of Erbil, but that has calmed since U.S. airstrikes began.

“We know the U.S. are strong and that they have to win here,” one Peshmerga soldier said. “They would not start this if they do not plan to finish.”