Civilians fleeing Falluja, an Iraqi stronghold of the so-called Islamic State, are being shot as they leave.
The Norwegian Refugee Council said families it had interviewed described people being shot dead as they crossed the Euphrates River.
The Norwegian Refugee Council that runs refugee camps near Falluja, said up to 50,000 people remained in the city.
Iraq's army began the fight to retake the city late last month.
Falluja lies just 50km west of Baghdad and has been held by IS since 2014. It is one of two remaining IS strongholds in Iraq.