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An estimated 20,000 children are trapped in the city of Fallujah as Iraqi forces continue their fight against so-called Islamic State, UNICEF has said.
There are warnings of a "human catastrophe" unfolding in the city, with around 50,000 civilians thought to the stuck with a lack of food, medicine, safe drinking water and electricity.
The UN have reported people starving to death in the city and being killed for refusing to fight for terror groups.
An aid agency has warned of a "human catastrophe" unfolding in the Iraq city of Fallujah.
Jan Egeland, head of the Norwegian Refugee Council, said only one family had managed to escape the besieged town on Monday.
"Warring parties must guarantee civilians safe exit now, before it's too late and more lives are lost", Egeland said.
Egeland's comments come on the day Iraqi forces repelled a four-hour counterattack, a day after entering the southern part of the city.
He added a lack of food, medicine, safe drinking water and electricity is "pushing families to the brink of desperation".
It is estimated that 50,000 civilians are still inside Fallujah and humanitarian groups have renewed calls on both sides to open up safe corridors for non-combatants to flee.
This appears unlikely as IS and the Iraqi forces need to agree on a cessation of hostilities - whilst Iraqi authorities want to prevent IS fighters from escaping the city by mixing with the fleeing civilian population.
British forces have carried out airstrikes in support of the Iraqi battle to free Fallujah from the so-called Islamic State.
The Ministry of Defence confirmed RAF aircraft attacked terrorist positions in the militant-held city on Monday, as Iraqi special forces launched their first ground assault on the territory.
The MOD said Tornados, Typhoons and remotely controlled Reapers offered air support to Iraqi troops in the days leading up to Monday's assault.
Stockpiles of terrorist weapons had been destroyed, including a building north-west of Fallujah where a "large group of terrorists" had been reportedly preparing for a counter-attack.
Fallujah is situated 40 miles west of Baghdad and has been under IS control for more than two years.
So-called Islamic State militants have been using "several hundred families" as human shields during the Iraqi army's assault on Fallujah, according to reports received by the United Nations refugee agency.
Around 3,700 people, including 624 families, have fled the city over the past week since the offensive to retake it from IS began.
"We have reports of casualities among people in the city centre in Fallujah due to heavy shelling, including seven members of one family on May 28," UNHCR spokesman William Spindler said.
"There are also reports of several hundred families being used as human shields by ISIL, in the centre of Falluja."
Around 1,300 people are staying in the al-Iraq camp in the Ameriyat al –Falluja district. The UNHCR understands some 500 men and boys aged over 12 are held for security screening.
Iraqi troops attempting to reclaim the city of Fallujah have repelled a four-hour attack by so-called Islamic State in the south of the city.
The attack started at dawn on Tuesday in the Nuaimiya area, according to special forces officers.
The officers said IS militants used tunnels, deployed snipers and sent six explosives-laden cars to hit the troops, but they were destroyed before reaching their targets.
The previous day Iraqi troops captured almost 85% of the ground in the same area when they first entered the city.
Fallujah, which has been under IS control for more than two years, is 40 miles west of Baghdad and is the last major city in western Iraq still under control of the group.
More than 20 people were killed and around 50 injured in three separate bombings that hit Baghdad on Monday, police and medical personnel said.
Twelve people were killed and more than 20 injured when a car bomb blew up in the northern Shaab Shi'ite district.
Eight were killed and 21 wounded by a suicide bomber who detonated a car near a government building and a police station in the district of Tarmiya.
A third bomb involving a suicide bomber on a motorcycle in Sadr City killed three people and injured nine.
The attacks came as Iraqi forces and Shi'ite militias fought so-called Islamic State militants in Falluja, around 66 km west of the capital.
The Iraqi army has stormed the southern edge of Falluja under US air support, and captured a police station inside the city limits.
An elite military unit, the Rapid Response Team, is leading what is shaping up to be the biggest assault ever fought against the so-called Islamic State.
Explosions and gun fire was reportedly seen in Naimiya, a district of Falluja on its southern outskirts.
Separately, Kurdish security forces announced advances against IS in northern Iraq, capturing villages from militants outside Mosul, the biggest city under militant control.
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Counter-terrorism forces, backed by Shi'ite militias on the ground and coalition airstrikes, are moving into the city on several fronts.