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Kurdish fighters after a clash with the Islamic State in March. They have managed to retake and hold significant territory. CreditIraq/Reuters 
SULTAN ABDULLAH HILLS, Iraq — Since retaking these barren hills in northern Iraq from the jihadists of the Islamic State, Kurdish pesh merga forces have dug in: excavating trenches, unfurling barbed wire and coordinating with the United States-led military coalition to identify targets for airstrikes.
The new outposts dotting the hilltops provide clear views of villages where Islamic State jihadists build truck bombs and launch attacks, but the Kurdish forces have no plans to advance, saying the territory is not theirs to fight for.
“Now our main job is defense,” said Maj. Gen. Mohammed Khoshawe, a field commander. “To defend the Kurds, this is the farthest we go.”
The ability of Kurdish forces in northern Iraq to retake and defend territory has been a rare success story for the Obama administration’s policy of coordinating with local ground forces to battle the Islamic State, also known as ISIS or ISIL. This week, the administration announced that it was considering expanding that effort with a network of new training bases in the Iraqi countryside.
Since the Islamic State’s breakout in Iraq last June put several Kurdish cities in peril, the pesh merga have benefited from a concerted campaign of airstrikes, as well as training, arms and intelligence support from the United States and its allies.
But the successes of the Kurdish forces also highlight the political and military limits that American policy faces elsewhere in Iraq and Syria, where the United States lacks a solid relationship with forces on the ground and where there is little unity.
Last month, Iraqi security forces surrendered the city of Ramadi to Islamic State fighters that numbered “in the low hundreds,” according to a senior official with the anti-Islamic State coalition. Local Sunni leaders complained that the Iraqi government had been slow to send reinforcements or supplies to help in the fight.
And longer-term efforts to muster forces to fight for Mosul in Iraq and Raqqa in Syria have made little progress, leaving the jihadists unchallenged in their two largest cities. That is in part because of American discomfort with aiding the groups that have proved among the most effective in fighting the Islamic State: Iranian-backed militias and rival jihadist groups, like the Nusra Front.
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TURKEY
IRAN
IRAQI
KURDISTAN
Tal Afar
SYRIA
Mosul
Sinjar
Raqqa
Erbil
Kirkuk
IRAQ
AREAS
UNDER
FULL ISIS
CONTROL
Tikrit
Ramadi
Baghdad
AREAS OF
ISIS INFLUENCE
Falluja
50 MILES
Towns with ISIS presence
Few in northern Iraq’s semiautonomous Kurdish region believe that the Shiite-led government in Baghdad will soon reform its armed forces or persuade Sunni Arabs living under the Islamic State to turn against it. And continued disagreements with the central government over budget issues have left many Kurds feeling that they are on their own against the jihadists.
So they have focused inward, scrambling to improve their forces and to secure the long and volatile border with their jihadist neighbors. Many hope that the battle will bring them closer to their long-term goal of founding an independent Kurdish state.
The pesh merga have evolved significantly from the out-of-shape force that nearly collapsed before the Islamic State last year into one capable of holding back the jihadists, according to pesh merga leaders, Western diplomats and coalition officials.
Coalition airstrikes have been essential in destroying Islamic State positions and paving the way for Kurdish advances. But on the ground, newly trained sappers have dismantled thousands of explosives; antitank missiles provided by coalition members have countered the Islamic State’s devastating truck bombs; and pesh merga fighters have helped identify targets for airstrikes, officials said.
One Kurdish commander said intelligence from an American drone had helped his men ambush and kill jihadists who were mining a front-line village.
Mustafa Sayid Qadir, the minister of pesh merga affairs, said that many of the force’s 160,000 fighters had been trained in urban combat, battlefield logistics and bomb disposal, improving their capabilities.
That had helped them advance, he said, putting them in control of 95 percent of the territory they want for a future independent state, including the oil-rich city of Kirkuk, which Baghdad also claims.
This has posed yet another hurdle for the American strategy against the Islamic State. Early hopes that the Kurds would help retake Mosul, just south of Kurdistan in Nineveh Province, have dwindled now that the pesh merga are focusing on defense, although Kurdish officials say they might contribute a force if such an assault becomes possible.
A senior official with the international coalition said the pesh merga’s capabilities had grown, but that few expected them to fight much elsewhere in Iraq.
“Their desire to advance farther is fairly limited now,” the official said, speaking on the condition of anonymity according to military protocol.
Particularly damaging to Kurdish forces was the Islamic State’s skill with explosives, both car bombs and roadside bombs, which accounted for most of the Kurds’ 1,200 casualties since last year.
Sirwan Barzani, a businessman and relative of the Kurdish president who commands a force southeast of Mosul, said his men had defused thousands of bombs in areas taken from the Islamic State.
He showed photos on his phone of scores of charges and showed off a cellphone wired to a fuse with instructions in Arabic on how to use it to detonate a bomb remotely.
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Where ISIS Has Gained Territory in Libya 

Islamic State fighters seized important locations around Surt. 
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Like other commanders, he complained of lacking weapons and praised the Milan antitank missiles provided by Germany for allowing the pesh merga to blow up truck bombs before they reached their targets.
“They have saved hundreds of lives of the pesh merga, thanks to God and thanks to the Germans,” he said.
One Western diplomat said the pesh merga was far from a professional army and that most of their advances were because of coalition airstrikes. Many of their fighters have not been paid in months, and the force is still divided between political parties, hampering cooperation.
Many commanders fear their region is still in danger and that Kurdish forces are spread too thin.
“The farther you go out, the harder it is to provide logistics,” said Polad Talabani, the head of the Kurdish counterterrorism unit. “We have more than 1,000 kilometers of borders with ISIS, so the equipment, vehicles and weapons we have are all very stretched.”
He said it was only a matter of time until the Islamic State attacked again, pointing to a recent coalition airstrike in the city of Hawija that detonated three large truck bombs he said were intended for an attack on Kirkuk.
“It was a huge, huge explosion,” Mr. Talabani said. “It would have been a disaster if those trucks had gotten anywhere close to Kirkuk.”
The deep ties between the Kurds and coalition were clear at General Khoshawe’s hilltop outpost 40 miles southeast of Mosul.
He recalled how he had struggled to identify an Islamic State position in a nearby village that kept firing on his men, killing seven of them over time.
Working with a French team from the coalition, his men had driven an armored car near the village to draw fire so the French team could pinpoint its source.
“A few minutes later, it was attacked by an airstrike that destroyed the whole building,” General Khoshawe said.
He also described how his men had used information from an American drone to ambush and kill Islamic State fighters.
Regardless of their successes, his men were busy digging in. A new road connected the string of sandbagged outposts, work crews were installing power lines and military tents were being replaced with concrete barracks.
When asked if the positions marked the outlines of a future Kurdish state, he replied, “Of course. These are facts on the ground.”