It was nearly the perfect heist. In June, Iraq's Kurds snuck in behind retreating government troops to grab long-coveted land and watched from their new borders as Baghdad and jihadists fought over the rump state.

But the move dragged Kurdistan's celebrated peshmerga out of their comfort zone and the cash-strapped force is now taking heavy losses along its extended front.

"They've bitten a whole chunk of cake that's going to take a long, long time to digest," said Toby Dodge, director of the Middle East Centre at the London School of Economics.

The autonomous region of Kurdistan in northern Iraq expanded its territory by around 40 percent when it took the slipstream of soldiers fleeing the onslaught the Islamic State launched on June 9.

Peshmerga troops initially took up positions right in front of IS territory and seemed determined not to get involved.

One video posted on the Internet shows jihadists and peshmerga on either side of the same bridge, looking quite relaxed.

But over the weekend, IS fighters attacked several of the peshmerga's new positions west and north of Mosul, killing several and forcing them to withdraw.

A statement the jihadist group issued on Monday appears to confirm that any non-aggression pact is over between the IS and the Kurds.

"Islamic State brigades have now reached the border triangle between Iraq, Syria and Turkey. May God Almighty allow his mujahideen to liberate the whole region," it said.

Kurdish political commentator Asos Hardi said the Islamic State "is aware that the United States is backing plans for Sunni-Shiite-Kurdish cooperation" against them.

"They are trying to secure the area where the borders of Syria, Iraq and Turkey meet but that cannot be achieved without trying to expand into Kurdish regions," he said.

Issam al-Faily, a political scientist from Baghdad's Mustansiriya University, said the Kurds should not assume that jihadists will not seek to enter their turf.

- Dangerous situation -

"Now IS is willing to expand on the land of Kurdistan, if they (the peshmerga) don't put an end to it quickly, the situation could develop very dangerously," he said.

The peshmerga are widely regarded as the most able military outfit in Iraq but the financial squeeze caused by their dispute with Baghdad over oil revenue is taking its toll.

That has constrained the Kurdish Regional Government's ability to pay and equip its troops properly.

"Militarily they're not capable, trained or funded in a way that would allow them to have control of that extra" territory, Dodge said.

In the town of Jalawla, which sits on the other extreme of the peshmerga stretched frontline, 130 kilometres (81 miles) northeast of Baghdad, Kurdish troops have taken some of their heaviest losses in recent days.

On several occasions, they fought for hours to hold a position, only to pull back for lack of ammunition.

In a matter on hours on Saturday, the peshmerga abandoned their positions in Zumar, two oil fields, the large town of Sinjar and other smaller towns and positions.

The Syrian Kurdish group PYD that crossed the border to come to their rescue on Monday said it briefly took in 700 peshmerga back into Syria to regroup.

"The peshmerga are well-trained, well-equipped and motivated, but definitely more efficient fighting in defensive positions, on their own terrain, than projecting into the plains of Arab Iraq," said Peter Harling, from the International Crisis Group think tank.

"Quite simply, they were never meant for that," he said.

Some analysts argued that the peshmerga did not fight to the death for Mosul's hinterland because they are pushing for Washington to step in and fill their budget gap.

"The peshmerga withdrawal was also tactical, as a way of pressuring the US to provide them with weapons that they are currently having to buy on the black market," said Ihsan al-Shammari, a professor at Baghdad University.

Such procurement theoretically requires approval from the federal government in Baghdad but Prime Minister Nuri al-Maliki appears to have definitively fallen out of favour with Washington.