"The raids were unexpected and, as Sadr City is a violent neighbourhood, some families are fleeing the area looking for displacement camps in the outskirts of the capital. Many of them have travelled to Najaf and Kerbala in the south," said Hussam al-Din, president of the Baghdad-based Iraqi Humanitarian Association for the Displaced (IHAD).
"Local NGOs are desperate because we cannot reach the area for security reasons and fleeing families are leaving their homes without enough money to support themselves," al-Din said.
NGOs are trying to help but say they would not be able to cope if families continue to flee the district, more so since most of the district's residents are poor, he added.
Some 400 may have fled
Al-Din believes that at least 400 Iraqis have already fled the district, most of them heading to southern provinces but he warned that the number could be much higher as insecurity is preventing aid workers from gaining access to the area.
"If this critical situation continues, we believe that by the end of the week dozens of other families will leave their homes in search of a safer place," he said.
The raids were part of a US-led forces' programme to target suspected members of a cell alleged to be smuggling sophisticated roadside bombs known as Explosively Formed Penetrators (EFPs) from Iran. At least 10 militants have been killed since Sunday morning and over 150 rounds of ammunition, components for roadside bombs and other ammunition, has been seized.
US officials have said that they have discovered a bloodstained torture chamber in a building in the Sadr City which they believe has been used for sectarian violence.
People's daily lives affected
"We understand how important it is to bring security to the capital but such raids are affecting people's daily lives and scaring hundreds of families who would rather be displaced than die in crossfire," said Fatah Ahmed, spokesperson for the Iraq Aid Association (IAA).
"Since Sunday morning, nearly 40 families from Sadr City have come to us seeking our help to find them a place to stay. But there is nowhere to send them; new displacement camps should be built to cope with their needs," he said.
Lack of medicines
Dr Bilal Abdel-Salam, a physician at Sadr City Hospital, said they lacked emergency medicines and would not be able to save lives should the situation deteriorate further.
"Conditions in the district will get worse if the raids continue and we need supplies to store in our hospital. We urge local NGOs to send us some emergency materials to prevent people dying from lack of assistance," Abdel-Salam said.
Families fleeing the district said they were living in dire conditions and could not stay in Sadr City to watch their loved ones get killed in crossfire or see their houses being destroyed with their families inside.
"We and some of our neighbours are fleeing to other districts of Baghdad and today others have left for Karbala in the south as they are scared of the raids. Militants have said they will fight the US troops and for sure when that happens the situation will get much worse, but we hope that we are going to be very far away when that happens in the coming days," said Sayf Mu'tazz, 38, a Sadr City resident who fled the district with his family.