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Iraq's al-Qaida-inspired militants who took over the city of Fallujah are now trying to show they can run it, providing social services, policing the streets and implementing Shariah rulings in a bid to win the support of its Sunni Muslim population.

Gunmen in ski masks and Afghan-style tunics patrol the streets, but also perform a sort of community outreach. On a recent day, they were seen repairing damaged electricity poles and operating bulldozers to remove concrete blast walls and clear garbage. Others planted flowers in a highway median, and some fighters approached residents in the street and apologized for gaps in services, promising to address them.

The Islamic militants have also made themselves the law in the city and aim to show they are acting to prevent crime. On Thursday, militants cut off the right hand of a man accused of robbing a mobile phone shop and paraded him through Fallujah in the back of a pickup truck, forcing him to raise his stump to show people, according to witnesses in the city.

The push by the al-Qaida breakaway group, the Islamic State of Iraq and the Levant, marks an effort to bolster their standing in a community that remains under siege and exhausted by three months of clashes between the insurgents and government forces.

The group is trying to increase its appeal among the broader Sunni minority in Iraq, where resentment against the Shiite-led government runs deep — and it is trying to correct past mistakes. In the 2007, many major Sunni tribes turned against al-Qaida militants and formed U.S.-backed militias to battle the group, angered by its rampant killings during the height of the country's sectarian bloodbath following the 2003 U.S.-led invasion. Many in the Sunni community still bitterly hate the militants, and some tribes have joined government forces in fighting the group in Fallujah.

Gauging whether the outreach is improving the group's image among Fallujah residents is difficult. Several residents who spoke to The Associated Press said they fear the militants and want police control to return. Some said they are happy with the group's activities, but all spoke on condition of anonymity, fearing for their own safety.

"The ISIL people are providing security to Fallujah residents after policemen left," said Abu Abdullah, a shop owner who offered only his nickname. He said shoppers can reach his store more easily after fighters removed blast walls blocking the street.

ISIL took control of Fallujah, one of the main cities in Iraq's western, Sunni-dominated Anbar province, in late December. The turmoil began when security forces arrested a Sunni lawmaker sought on terrorism charges, then dismantled a year-old Sunni anti-government protest camp. Clashes erupted with security forces.

To ease tension, the government ordered the army to hand over security duties in Anbar to local police. But militants took the opportunity to drive out the police and overrun Fallujah, just 65 kilometers (40 miles) west of Baghdad, and parts of the nearby provincial capital, Ramadi.

Nearly three months later, government forces have been unable to retake Fallujah. Government offices have been shut and a number of police stations have been demolished. Only schools and the directorates of health, electricity and the municipality remain operational, according to residents.

Control rests with two groups: ISIL and the Military Council For Tribal Revolutionaries. The tribal council is a mixture of tribal representatives and militants drawn mainly from the Saddam-era army. They don't pledge allegiance to ISIL, but avoid confronting them. ISIL was al-Qaida's main affiliate in Iraq but was recently disavowed by the global terrorist group after it expanded to fight in the civil war in neighboring Syria.

ISIL fighters in Fallujah protect key buildings such as banks and real estate offices. Recently, a senior ISIL leader joined local officials and tribal leaders in reopening a primary school. He expressed a readiness to help with fix up the school, provide it with desks and chalkboards, and offer protection.

With the collapse of the judicial system, they established a religious court to solve disputes among residents.

The hand amputation underlined the group's intention to show a tough-on-crime approach. But apparently to avoid alienating residents, ISIL has so far avoided enforcing some of the other most extreme aspects of its hard-line interpretation of Islamic law, overlooking some practices it considers "haram," or forbidden, several residents said. Barbers who trim beards are not being closed down, and women — who usually wear headscarves in the conservative city — are not forced to take on the even more conservative face-veil, for example.

To reach a broader Sunni audience, the militants are posting online clips of their social activities.

In one video, masked gunmen roam the streets in a pickup truck. They stop to knock on doors to hand out aid parcels and to hire a taxi for two women, paying the driver for them.

ISIL has pushed a similar online hearts-and-minds effort in Syria, where it controls the city of Raqqa, near the border with Iraq, and other pockets in northern Syria. It posted videos purporting to show ISIL members there sponsoring games such as musical chairs and telling jokes to laughing crowds. Another video from Syria showed ISIL members distributing food to needy people in a refugee camp and giving money to a female beggar.

But in Raqqa, many residents have said they live in fear of the group. It has taken a heavy hand in imposing Shariah in Raqqa, forcing women to wear veils over their faces and carrying out executions in public squares.

Anbar provincial councilman Faleh al-Issawi said ISIL's outreach in Fallujah "will do no good to polish the dark and savage image of al-Qaida," saying the people of Anbar will not forget al-Qaida's past "killings and crimes."

"Fallujah will always want to be part of the Iraqi state," al-Issawi told the AP in a telephone interview from Ramadi.

While in Iraq, the U.S. forces faced a stubborn insurgency in Anbar, mainly in Fallujah, where they fought two major battles in 2004 and suffered heavy causalities, going house-to-house for weeks to clear out militants in some of their heaviest urban combat since the Vietnam War.

Iraqi Prime Minister Nouri al-Maliki has tried to counter the militants' message. His Shiite-led government pledged millions of dollars to compensate those whose properties were damaged in fighting and to help more than 10,000 families uprooted from their houses.

In an ad on state TV, al-Maliki's voice booms through military loudspeakers as soldiers are shown gearing up and boarding helicopters to join their comrades on tanks and Humvees in an open desert area that resembles Anbar.

"The responsibility of protecting our country and people is yours," al-Maliki tells the troops. "We are with you, standing in the same trench to defend Iraq and Iraqis."

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