More than 43,000 people have fled the western Iraqi city of Fallujah since government forces launched an offensive to recapture it from the Islamic State extremist militia in mid-May, a UN agency said on Tuesday.
Over 10,000 of those fleeing the city left between Saturday and Monday, the International Organization for Migration (IOM) said.
A humanitarian group active in the area meanwhile warned that the journey for those fleeing the city was "still full of risks and extremely unsafe."
"Thousands" of civilians remain trapped inside the city, with gunmen reportedly preventing some fleeing the area, the Norwegian Refugee Council said.
Allegations that powerful pro-government Shiite militias have in some cases tortured and killed civilians fleeing the Sunni-populated city have sparked an angry response in Iraq.
On Monday Suhaib al-Rawi, the governor of Anbar province which includes Fallujah, said that the militias had killed at least 49 civilians, with another 643 missing after being subjected to torture.
Members of one family from near Fallujah have told dpa that 17 young men and boys from their family group were shot dead by militiamen in police uniform after giving themselves up.
Prime Minister Haider al-Abadi last week vowed that those responsible for the alleged abuses would be punished in accordance with the law.
Civilians fleeing Fallujah have told dpa of being exposed to artillery fire during the dangerous journey between government and Islamic State lines.
Al-Abadi announced the offensive on Fallujah on May 22. The city, in the Anbar province some 50 kilometres west of Baghdad, is a long-standing stronghold of Islamic State.
Iraqi forces are also engaged in an offensive in the north near the city of Mosul, although analysts say they are unlikely to be in a position to attempt to take Mosul itself for some time.
The IOM reported that while civilians continued to flee Fallujah, almost 70,000 other displaced people had returned home in May, including 33,000 returning to parts of Anbar recaptured by government forces.
Some 3.3 million people are still displaced in Iraq, the agency said.