About 35,000 refugees, believed to be mainly Syrian Kurds, have entered Iraq since last Thursday, the UN refugee agency UNHCR said.
At least 5,100 people crossed the border on Tuesday, fleeing the civil war in Syria.
This new exodus from Syria is among the largest we have seen in the conflict
Jumbe Omari Jumbe of the International Organisation for Migration (IOM) told reporters in Geneva that refugees arriving at two border crossings in the region were exhausted and dehydrated after walking long distances in spiralling desert temperatures.
He said the Kurds feared attacks by various armed rebel groups including al-Qaeda-linked Jabhat al-Nusra.
“Jabhat al-Nusra are killing and threatening us every day. They want the Syrian Kurds out of Syria. We have nothing left in Syria to live on,” Noursheen Nowzad, a refugee who fled Syria with six family members, told Al Jazeera.
Both al-Nusra and the Islamic State in Iraq and the Levant have in recent months been fighting for control of parts of northern and northeastern Syria against Kurdish groups who have taken advantage of the war to assert their control over majority-Kurdish areas.
The influx began last Thursday when the Kurdistan regional government authorities in northern Iraq opened access across the newly-built Peshkhabour pontoon bridge, UNHCR said. The bridge has now been reserved for commercial traffic and refugees have been directed to use the Sahela crossing to the south, it added.
“This new exodus from Syria is among the largest we have seen in the conflict,” UNHCR spokesman Dan McNorton told reporters.
Al Jazeera’s Imran Khan, reporting from Sahela, witnessed chaotic scenes as the refugees were to be transported by bus to camps in the town of Erbil.
“Trying to move these people to camps is a difficult business and in the fierce sun, tempers often flare," he said.
“The UN wants women and children to go first, but the procedure has broken down. So now the buses are mobbed.”
Nearly half the estimated 4,800 people who crossed on Monday were children, the UN Children's Fund (UNICEF) said.
UNICEF has identified at least 80 unaccompanied teenage boys sent across the border by their families for safety or to find work.
“Many are below 12 years old, and the younger ones were particularly dehydrated and exhausted after the four or five hour walk across the border in the scorching heat,” UNICEF spokeswoman Marixie Mercado said.
More than 1.9 million Syrians have fled to neighbouring countries and North Africa since the uprising began in March 2011 and Syria descended into civil war.