IRBIL, Iraq — As foreign powers jostle for control of northeast Syria, a new wave of refugees is trudging into Iraq, fearful, uncertain and worn out.

Aid groups said Wednesday that more than a thousand Syrians had crossed the Iraqi border in the days since U.S. troops pulled back and Turkey moved in to push Kurdish-led forces from its southern frontier. Should the violence worsen, humanitarian agencies are preparing to receive as many as 50,000 people by January.

Squatting in the shade of the northern Domiz camp’s spartan portacabins this week, many of the new refugees looked shellshocked. Children were jittery, their parents too tired to speak much.

The Turkish-backed offensive did not come as a shock — the refugees said they had been glued to the news, watching with rising dread the Turkish threats against the Kurdish-led administration that ran their area. But when the fighting finally began, its speed took many by surprise. In less than a week, more than 160,000 were fleeing, and those with permission to stay in Iraq headed straight there. 

Those without queued for days at the border. Many turned to smugglers, paying exorbitant prices for an hours-long walk through the night.

Salhar Omar Saffar, 30, said she scooped up her young daughter and ran.

“My mother stayed. She said she was too old to make the journey,” Saffar said. “But she told me to go. She told me to take the baby and to find a way to give her a life.”

The Norwegian Refugee Council said 1,006 people had crossed into Iraq since hostilities began Oct. 9.

“We expect more and more in the coming days,” spokesman Tom Peyre-Costa said. Most international aid groups said this week that the violence and insecurity had forced them to suspend humanitarian operations and evacuate foreign staff. The bombing and shelling also led hospitals to close and left areas without access to clean drinking water.

“Winter is coming, and with harsh conditions in Syria, displaced people will be more and more likely pushed to migrate towards Iraq, where they can seek shelter,” Peyre-Costa said.

The Kurdistan Regional Government, which administers Iraq’s northern province, called on the international community Tuesday to provide fresh support as the area prepared to receive a “new wave of displaced people fleeing conflict and persecution.”

After eight years of war in Syria, Iraq is home to 250,000 refugees. Tens of thousands more Iraqis remain displaced by the U.S.-backed fight against the Islamic State here. The United Nations said Wednesday that it was reactivating a camp in Bardarash, east of Mosul, to accommodate the new influx. Camp authorities have worked through the night to turn the lights back on and set up tents to house families. Guards and humanitarian staff in Domiz said they had been working 14-hour days to help the new refugees settle in.

The Trump administration’s decision to pull troops from northeastern Syria has set off a scramble for power there. As the Turkish military shelled border towns this week and an allied Syrian rebel force moved in, Russia brokered the only deal that Kurdish-led authorities had left, Western diplomats said: a partial return for Syrian President Bashar al-Assad’s forces and a likely end to the years-long Kurdish governance project there.

As the contours of that agreement remained unclear Wednesday, Turkey rebuffed U.S. calls for a cease-fire and pushed on with its offensive, demanding that the Kurdish fighters lay down their arms.

Few Syrian Kurds who crossed the border this week said they expected to return home any time soon. One man, who spoke on the condition of anonymity out of fear for his family’s safety in Syria, said he had stayed in their hometown through eight years of war, dropping out of school, hiding from militants and watching the futures they had hoped for ebb away. In the end, he said, his family left with smugglers Sunday night because they had a right to “live without war.”

His 19-year-old wife nodded.

“We are young people, and we’ve already lost our childhoods,” she said. “Syria is over for us. We just need to be anywhere else.”

For Saffar, too, Turkey’s offensive seemed to mark an end to life as she knew it in Syria. 

“I’m not going back. How can I? We lived eight years there as if there was freedom.”

She gestured toward her daughter, Silina.

“I never thought I’d leave my country, but I left it for her,” she said. “I walked through the mountain for her.”