Islamic State militants left Ramadi's streets and buildings boobytrapped with bombs, hampering efforts to rebuild the city two weeks after Iraq's elite counter-terrorism forces claimed victory against the militant group there, officials said.

Ramadi, the capital of Anbar province, was touted as the first major success for Iraq's army since it collapsed in the face of Islamic State's lightning advance across the country's north and west 18 months ago.

The militants have been pushed to Ramadi's eastern suburbs, but almost all of the city, which was battered by U.S.-led air strikes against Islamic State, remains off-limits to its nearly half a million displaced residents, most of whom fled before the army advance.

"Most areas are now under the security forces' control," Anbar governor Sohaib al-Rawi said on Saturday at a temporary government complex southeast of the city.

"Most of the streets in Ramadi are mined with explosives so it requires large efforts and expertise," he said.

Specialized bomb disposal teams from the police and civil defense force would begin work "soon", he said.

The counter-terrorism forces which spearheaded the city's recapture are securing only main streets and tactically important buildings, security sources said.

They have built up earth banks at the entrance of central neighborhoods deemed clear of militants but still laden with explosives, and marked buildings' exteriors as "mined", the sources added.

Snipers have also slowed progress. Iraqi forces clear them by calling in devastating air strikes - more than 55 in the past two weeks, according to the coalition.

On Saturday they routed militants from the Mal'ab neighborhood, adding the last major district in Ramadi's city center to their control, said commander Lieutenant General Abdul Ghani al-Assadi.

Iraqi forces withdrew from Ramadi in May last year, allowing Islamic State to take control, the group's biggest gain since sweeping across the Syrian border a year earlier and declaring it was establishing a caliphate.

Islamic State fighters are still holed up in a roughly 10 kilometer (6 mile) stretch east towards Husaiba al-Sharqiya using agricultural lands to evade detection, security sources said. It could take at least 10 days to clear those areas.

PATH OF DESTRUCTION

Hundreds of air strikes since July, combined with Islamic State sabotage, have reduced much of Ramadi to rubble.

The United Nations Development Programme (UNDP) is still waiting for the green light from the Iraqi government to enter the city and start work to rebuild it, the deputy head of its Iraq program, Lise Grande said.

UNDP has prepared 100 generators and mobile electrical grids to provide a temporary power grid as soon as that happens. An assessment of the damage to the rest of Ramadi's infrastructure will dictate other areas of focus.

The city will require around $20 million immediately for emergency humanitarian response and billions more for long-term reconstruction, said Grande.

"Restoring infrastructure is hugely important, but the decisive factor in getting people to return is when they think security is in place," she said.

After Ramadi, there remains the bigger challenge of Mosul, 400 km (250 miles) north of Baghdad. As many as 3,200 Islamic State fighters are there, more than three times the number that held Ramadi, according to the coalition.

It is also more densely populated. Most of Mosul's pre-2014 population of about two million have not left.

The destruction in Ramadi has sparked criticism including from powerful Iranian-backed Shi'ite militias, which were kept out of the battle for fear of stirring sectarian tensions in Anbar's Sunni heartland.

Despite accusations of human rights abuses, groups like Asaib Ahl al-Haq claim they have could have retaken Ramadi more "neatly".