Latest figures from the UN refugee agency, UNHCR, show the number of Iraqis fleeing their homes is rising.
An Iraqi girl prepares food at a refugee camp in northern Iraq
The latest figure is 60,000 per month, compared to a previous level of 50,000, a UNHCR spokeswoman said.
The body estimates 4.2m Iraqis have been displaced since the 2003 invasion. Of those, two million have gone abroad.
Of those displaced inside Iraq, more than half have fled since the Samarra mosque bombing in February 2006, which sparked a wave of sectarian conflict.
UNHCR spokeswoman Jennifer Pagonis said many Iraqis were struggling to get the basic necessities for daily life.
"Iraqis are finding it harder to get access to social services inside Iraq and many Iraqis are choosing to leave ethnically mixed areas before they are forced to do so," she said.
"Some Iraqis who stayed in the country until the end of the school year recently started leaving the country with their families."
Syria estimates more than 1.4m Iraqis are now within its borders. Jordan says as many as 750,000 are on its territory.
Both countries have complained about the burden the refugees are placing on their health and education systems.
An Iraqi boy arrives for his first day at school in Amman, with his father
The UNHCR has registered more than 170,000 refugees in the countries neighbouring Iraq.
Although the organisation has referred more than 13,200 of Iraq's most vulnerable cases to other countries for resettlement, only several hundred have actually been admitted to third countries.
The body has urged resettlement countries to make decisions more quickly so more refugees can start to rebuild their lives.
A key aim for UN agencies is to ensure Iraqi children receive education in their host countries.
More than 40,000 Iraqi refugee children started school in Jordan this month for the first time since they fled their homeland.
The UNHCR and the UN children's fund, Unicef, are appealing for contributions to a $129m (£65m) education programme for Iraqi children in Syria and Jordan.
On Tuesday, the US Assistant Secretary of State Ellen Sauerbrey announced a $30m contribution to the fund.
Also on Tuesday, Germany pledged US $5.4m to Syria to help it cope with the influx of Iraqi refugees.