Many of the families had made a brave dash for safety across the front lines to escape attempts by retreating Islamic State fighters to take them as human shields.
But the men who got away have now been detained by Iraqi security forces for investigation, in a reminder of the deep suspicion with which those who have been living under Islamic State rule are regarded by the Iraqi government.
The Iraqi army launched a new offensive on Thursday to recapture the remaining Ramadi neighborhoods still held by the Islamic State. Iraqi military officials estimate that around a quarter of the city is still in militant hands, and U.S. officials say as many as 400 to 700 Islamic State fighters are still holed up in the Ramadi area, including in the city center.
"It's tough to determine the current enemy head count remaining in downtown Ramadi at this point, given the dynamic nature of the last few weeks," said Col. Steve Warren, the U.S. military spokesman in Baghdad, in an email.
The Islamic State does not have the ability to recapture the city, but fully securing it could "take some time," he said. "Every house is potentially booby-trapped and must be checked."
There is also unexploded ordnance strewn around the streets, and water and electricity facilities are badly damaged, according to the U.N. High Commissioner for Refugees (UNHCR), meaning it could be even longer before it is safe for residents to return.
The Iraqi army retook most of the city on Monday, including the compound housing the provincial government, in a big boost for Prime Minister Haidar al-Abadi and for the demoralized government security forces.
Most of the 400 or so people who managed to escape the fighting are being sheltered at a camp for displaced people in the Anbar town of Habbaniyah, which is under the control of Iraq's Shiite-dominated government. Islamic State fighters are Sunnis.
Aysha Mohammed, 31, described how Islamic State fighters came to her neighborhood as the Iraqi army closed in and ordered families to accompany them as they retreated to another part of the city.
"They knocked at the door and told my husband to prepare for us to leave with them, because the Rawafidh and infidels are coming to kill us all," she said, using a derogatory term for Shiites.
So close were the advancing Iraqi army soldiers, however, that Mohammed and her family could hear the voices of the soldiers, shouting through loudspeakers and urging residents to escape. They decided to make a run for it.
"We waited until ISIS went to another alley, and we all left together. Me, my husband and my children were running together with other families, around 15 in all," she recalled, using an acronym for Islamic State. "We ran for about 10 minutes. We were afraid that ISIS would shoot us, but they didn't see us."
After they reached army positions, the men were separated from the women and children and taken away - 76 from among the 400 or so people housed at Habbaniyah, according to Iraqi officials.
"I just want my father to come back to us. He is not Daesh," said Zaid, Mohammed's 7- year-old son, using another acronym for Islamic State. He said his family had hated living under the militants.
"I saw them whipping people in the market. It made me afraid," said Zaid, who stopped studying after the Islamic State took over last May because they closed all the schools. "They cut off someone's head in front of people. I didn't see it, but I heard about it."
Souad Salih, 19, said she and her husband had been yearning to leave for months, but the Islamic State refused to allow anyone to depart from the town.
"They treated us like prisoners, she said. "When we heard the Iraqi army was coming, we were very happy, but at the same time afraid because of the war. We were praying that ISIS would just run away and leave us alone, but they tried to take us with them."
"I am very happy right now. Even though I am living in a camp, at least I am not among the savages," she added. "I just hope my husband will join me soon."
Falih al-Issawi, the deputy head of the Anbar provincial council, said he was personally supervising the interrogation of the detained men. He promised that "all of those who are innocent" will be released.
Not all are, however, he added, describing how an 8-year-old boy had informed on his father, telling authorities the man had been working with the Islamic State.
And not all of the families in Ramadi managed to escape. The Islamic State is still holding more than 200 families as human shields, Karhot said. One group of people tried to escape on Wednesday, but Islamic State fighters saw them and opened fire, killing many of them, he said.
According to Hamid al-Dulaimi, the mayor of Ramadi, the families still being held hostage are "the main obstacle" to recapturing the rest of the city. "They are being used by Daesh as human shields," he said.
© 2015 The Washington Post