Civilians fleeing Falluja, an Iraqi stronghold of the so-called Islamic State (IS), are being shot as they leave, an aid agency says.
The Norwegian Refugee Council (NRC) said families it had interviewed described people being shot dead by IS as they crossed the Euphrates River.
The NRC, 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 (30 miles) west of Baghdad and has been held by IS since 2014. It is one of two remaining IS strongholds in Iraq.
Shakir al-Essawi, the head of Falluja's regional council, told Reuters people were trying to cross the Euphrates in refrigerators, cupboards and barrels.
"Our biggest fears are now tragically confirmed with civilians being directly targeted while trying to flee to safety," said Nasr Muflahi, the Iraq country director of the NRC, in a statement which said "armed opposition groups" were behind the shooting.
"This is the worst that we feared would happen to innocent men, women and children who have had to leave everything behind in order to save their lives."
Iraq's army said on Sunday it had all but encircled Falluja, with only the western bank of the Euphrates not under its control.
The latest area secured by Iraq's military, with the help of US-led air strikes, was the southern district of Naymiyah, Associated Press reported.
Iraq's Prime Minister Haider al-Abadi said last week that the offensive had been slowed down to protect people still inside Falluja.
Other Iraqi officials have said IS is offering stiff resistance as troops push towards the city centre.
In other developments:
- the Agence France-Presse agency reported on Sunday that a mass grave containing up to 400 bodies, thought to be soldiers killed by IS in 2014 and 2015, was found in the town of Saqlawiya, north of Falluja
- at least four people drowned as their boat sank while they were trying to flee across the Euphrates
- the NRC said almost 3,000 people had reached refugee camps since 21 May
Falluja - key facts:
- had population of more than 300,000 before it was seized by first al-Qaeda and then by IS in 2014
- has always been a hotbed of Sunni defiance, becoming a symbol of resistance to US forces in violent battles in 2004
- controls main highway from Baghdad to both Jordan and Syria
- is known as the "city of mosques" - more than 200 mosques in city and surrounding area