The government of Iraqi Kurdistan has set an entry quota of 3000 refugees per day to cope with an influx of people fleeing the civil war in Syria.
About 35,000 refugees, believed to be mainly Syrian Kurds, have entered Iraq since last Thursday and camps there are struggling to cope.
The UN refugee agency says more than 5000 arrived on Monday.
It said they arrive exhausted and many are dehydrated from walking in the scorching heat.
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.