Iraqi and Kurdish forces have relied heavily on U.S.-led coalition jets as they have won back territory from the Islamic State.

But now, in the country’s largest offensive since the 2003 invasion — the campaign to recapture Mosul from Islamic State militants — some say they aren’t getting what was promised.

Iraqi army commanders advancing from the southeast complain that they have been forgotten, while even members of the counterterrorism forces, who work closely with the U.S.-led coalition, said air cover was disappointing on their first day in the fight.

A Kurdish security official, who spoke on the condition of anonymity because of the sensitivity of the topic, said that the air support was “very limited” and that Kurdish forces had taken heavy casualties as a result when they opened a new front on Thursday.

U.S. officials say they have large amounts of air power backing the push for the city, which was launched on Monday, but there are more fronts to support than ever before in an operation against the militants. Tens of thousands of Iraqi troops are closing in on the city from the north, south and east, and coalition jets are also bombing militants across the border in Syria.

Iraqi forces gather after the liberation of a village from the Islamic State south of Mosul on Oct. 21, 2016, during the operation against the militants. (Thaier Al-Sudani/Reuters)

[Battle for ISIS stronghold could trigger new crisis: A million displaced Iraqis]

In previous offensives in Fallujah, Ramadi and Sinjar, Iraqi forces have become accustomed to close air support, with coalition jets clearing the way for their advance by flattening enemy artillery and mortar positions and eliminating car bombs that speed toward their lines. The heavy air backing has boosted the confidence of Iraqi and Kurdish forces but also has left them dependent on the help.

“Mosul is the largest operation conducted to date; there are a lot more targets, more axes of attack,” said Col. John Dorrian, a spokesman for the U.S. military in Baghdad. “One of the immutable truths of air support is that there will always be more demand than supply.”

The coalition is working with Kurdish and Iraqi forces to better “sequence” operations to resolve the issue, he said.

About 25 miles southeast of Mosul, on the front lines near the town of Gwer, there were steady complaints from soldiers from the 9th Armored Division of Iraq’s army, which has been grinding north up the eastern bank of the Tigris River.

Across the radio in a Humvee touring the area came regular pleas for strikes. “American support is bad, bad, bad,” said Sgt. Marwan Abbas.

In a temporary headquarters in the village of Kanhash, the division’s commander, Lt. Gen. Qassim al-Maliki, chose his words carefully at first.

“There is support, but a lot of the time it’s delayed,” he said. But then a call crackled through on the radio from a soldier requesting airstrikes after a rocket-propelled grenade hit his tank.

Maliki sighed and turned.

“There is no support,” he said. “Do you see any planes in the sky?”

It is unclear how many aircraft from the United States and its coalition are dedicated to the fight in Mosul, but a senior defense official said the number was “significant.”

Footage of the battle has shown an array of U.S. aircraft flying overhead, from B-52 bombers to Apache gunships.

The targeting process for airstrikes in Iraq can be unwieldy as requests for air support need to flow from local forces on the ground to a joint U.S.-Iraqi command center. From there, aircraft need to verify the targets before striking.

Maliki said the two observation drones used by the coalition to spot targets were not sufficient for his sector of the Mosul battle, which includes 40 villages and towns that need to be cleared.

His deputy, Brig. Gen. Walid Majid, complained to joint operations command in Baghdad.

“If they are not going to support us, it would be better if they just told us,” he said.

The militants have put up a ferocious defense for villages and towns outside Mosul. On Friday, they also staged a brazen attack on the northern Iraqi city of Kirkuk, in what local officials said was an attempt to divert attention and security forces’ resources.

[Islamic State forces attack Iraq’s oil-rich city of Kirkuk]

The Kirkuk governor, Najmiddin Karim, said Kurdish helicopters were called in to put an end to the incursion. Coalition jets also struck in the area.

In Mosul and the surrounding province of Nineveh, the targets destroyed by coalition strikes on Thursday included 23 militant fighting positions, nine car bombs, six buildings, a headquarters, seven vehicles, two staging areas, two checkpoints and five Islamic State tactical units, the coalition said.

But stretched across such a wide area of battle and enemy-held territory, the support still felt sparse or slow to some.

The Kurdish official said air support was “virtually non-

existent” in some areas as around 10,000 Kurdish soldiers known as peshmerga launched a new offensive from the north. “This is ridiculous,” he said. “We expect much more from the coalition.”

Peshmerga forces released a pointed statement noting that an unspecified number of troops had “paid the ultimate sacrifice” and that coalition air cover was “not as decisive as in the past.”

A senior defense official, speaking on the condition of anonymity, said commanders are “aware of the concern.”

“It’s something we’re talking to the [peshmerga] about to examine the situation to see what resources we do have and if there are opportunities to provide support in additional ways.”

Brett McGurk, the State Department’s envoy to the coalition, said that there had been a large number of airstrikes the day after the Kurdish complaint.

“Massive coalition airstrikes today on the #Mosul fronts,” he tweeted Friday. The coalition was also supporting the peshmerga and assisting to “wipe out” infiltrating Islamic State cells in Kirkuk, he added.

Col. Falah al-Obedi, whose elite counterterrorism forces entered the battle for the first time Thursday in the town of Bartella, said coalition support “was not at the required level.”

“It wasn’t at the level of Fallujah, it wasn’t the level of Beiji or Qayyarah,” he said, listing previous offensives. “They let us down.”

Gibbons-Neff reported from Ankara, Turkey, and Abu Dhabi. Mustafa Salim in Kanhash and Irbil, Iraq, contributed to this report.

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