UN Secretary-General Ban Ki-moon says there is "a great risk" to about 50,000 civilians the UN estimates are still in Fallujah, especially for those trying to flee the Iraqi government offensive to retake the city from the Islamic State extremist group.
UN spokesman Stephane Dujarric said Monday "it's important that they have some safe corridors that they could use."
He called the situation in and around Fallujah "very fluid."
The United Nations is providing emergency assistance including water, shelter and food to those who make it out, Dujarric told reporters in New York.
He said authorities are transporting a lot of displaced woman and children to Amiriyat al Fallujah, about 30 miles south of Fallujah, while men and boys are reportedly being transported by Iraqi authorities to central Anbar for security screening.