A strapping US soldier, his flak jacket draped with weaponry and his rifle pointed at his feet, extends an application for a small business grant to Iraqi shopkeeper Warad Mutaab Qaataa.

Qaataa, a balding, soft-bellied man, watches nervously from across his tiny living room as Captain Beau Hunt tells him how to apply for up to $2,500 (Dh9,813) to enlarge the small shop he runs from his home in Sadr City, a sprawling Baghdad slum.

Not long ago, US soldiers raided his home at gunpoint at night. Now, they are back offering cash.

Qaataa says business is picking up slowly. "Of course, the situation is far better than it was," he said.

The grant is one small part of the US push to resurrect this mainly Shi'ite area that until a few months ago was in the iron grip of the Mehdi Army – the feared militia loyal to anti-American cleric Moqtada al Sadr.

Sadr has quietened since fierce fighting this spring allowed US and Iraqi troops to take control of the area, a major boost for the US-backed government of Prime Minister Nuri Al Maliki.

Sadr, whose defiance was a rallying cry for many poor and disaffected members of Iraq's Shi'ite majority, has ordered his troops to cease fire and now signals he could dissolve his militia entirely if the US withdraws its 144,000 troops according to a timeline. US troops say the best way to ensure the fighters don't come back is to improve life in Sadr City, where power flickers on a few hours a day and rotting trash piles on curbs.

In the slum – once called Saddam City – squatters cobble together homes out of cinderblocks. In one dusty alley, a barefoot child picks his way through a green river of sewage.

US military officials say they are spending $108m in Sadr City, $81m from US taxpayers and $27m provided by the Iraqi Government from oil revenue.

So far they have spent about $20m refurbishing schools and clinics, overhauling roads and improving decrepit sewage systems. They have turned dusty lots into grassy soccer fields and will soon reopen the area's sole swimming pool.

But they acknowledge it is only the barest beginning for the slum of two million people that has suffered decades of neglect. The reconstruction projects in Sadr City reflect efforts across Iraq to repair the wounds of war, modernise infrastructure and create investment and growth. "We want to rebuild Iraq from zero," Maliki said recently.

Five years after the US invasion, many Iraqis go without the most basic services. Critics point the finger at Washington, which failed to protect critical infrastructure and provide fundamental services, especially in the chaos after its arrival.

Iraq's Government has pledged $100m to rebuild Sadr City and has set aside $3bn for Baghdad. However, Baghdad security spokesman Tahseen Al Sheikhly says the capital needs $30bn and the country needs $400bn.

Given the painfully slow pace of reconstruction spending – blamed on Iraq's impenetrable bureaucracy, a lack of experienced officials and ongoing violence – it may take some time until any plans become a reality.

Meanwhile, US soldiers in Sadr City quietly express frustration with the government's plodding steps on major projects.

American forces hope their projects will deter new violence and prevent renewed support for the Mehdi Army, which built its following in part by providing medical care and social services.

On a tour of US-backed projects, civil affairs officer Sergeant Michael Horst peers into a shadowy room that was once a science lab at a girls' high school.

Damaged in the clashes, dust blankets workstations, windows are shattered and rubble is heaped in a corner. But the sharp smell of fresh paint wafts through the school. Workers weld new classroom doors while others plaster a damaged ceiling.

"This is the only way we can show people there's no reason to go back to the Mehdi Army," said Captain Andrew Slack, who heads a US unit patrolling southern Sadr City.

US forces are also hoping more Iraqis will provide intelligence that will help them snare militiamen. That means some US projects come with a quid pro quo. "We've got to keep security in this area. This is where I need your help if you see anything bad," Hunt tells Qaataa as he sits in the Iraqi's living room.

The shopkeeper simply nods.