BEIRUT — An outpouring of civilians from the Islamic State’s final redoubt in eastern Syria has pushed displacement camps to the “breaking point,” an aid group said Friday.

The International Rescue Committee reported that at least 12,000 women and children had been transported to the al-Hol camp since Wednesday. More than 55,000 have arrived since the U.S.-backed military operation announced its final assault on the Islamic State stronghold in early December.

U.S.-backed forces and Western diplomats said this week they were confounded by the sheer number of fighters and families trudging out of Baghouz, a hamlet in Deir Ezzor province that has been surrounded for weeks and is believed to encompass less than a square mile of Islamic State-held territory.

Aid groups have been left scrambling. As suspected fighters have been trucked off for interrogation in bursting prisons, the daily influx of women and children evacuated from Baghouz have overwhelmed humanitarian teams in the al-Hol camp.

“No one could have guessed that such a large number of women and children were still living in Baghouz,” said Misty Buswell, an advocacy director for the IRC. “The IRC and other agencies are doing all they can to help the arrivals, but al-Hol camp is now at a breaking point.”

Aid workers say al-Hol and the nearby al-Roj camp were unprepared for the tens of thousands of people who have arrived, and a significant number of families have been left without tents, water or adequate food supplies.

Four years after the Islamic State commandeered a stretch of Syria and Iraq the size of Britain, the group’s fighters are pinned down in a nondescript patch of land close to the Iraqi border.

The U.S.-backed Syrian Democratic Forces said this week they were close to victory in Baghouz but cautioned that the fighting was being slowed during daylight hours. But with better firepower and equipment, the SDF is making progress under the cover of darkness, aided by a campaign of U.S.-led airstrikes. The battle is expected to end in the coming days.

As militant fighters and civilians have surrendered themselves, they have continued to chant fealty to the Islamic State, according to videos taken inside SDF-held areas, and told reporters on the scene that the so-called caliphate is not defeated despite its loss of territory.

The families sent to the displacement camps face an uncertain future. Scores of children, most of them infants, have died on the road to al-Hol in recent weeks, say the IRC and UNICEF. Ten death certificates reviewed by a Washington Post reporter said most had died of pneumonia after being transported on the back of flatbed trucks during an hours-long drive in winter temperatures.

“We have seen a staggering number of children die on the journey,” Buswell said. “Unfortunately, this figure could be the tip of the iceberg.”

While a small number of Syrians have returned to their home cities after family members vouched for them, tens of thousands of Iraqis and other foreigners remain in limbo.

The United States and most European countries have expressed reluctance to repatriate their citizens, while the SDF insists it cannot hold them indefinitely.

During a recent visit to al-Hol, the camp’s reception areas were packed with women and children under the age of five, many of them appearing to suffer from health complications. Families interviewed in the hastily constructed concrete structures said that they had been sleeping on the floor for at least a week. The rooms smelled of sickness and defecation.

“It’s a disaster, we can’t hold all these people,” said one aid worker, speaking on the condition of anonymity because he was not authorized to speak to the press. “We’re Syrians running these camps. Foreign countries can say they won’t help, but we didn’t ask for them either.”