Fallujah residents facing 'humanitarian disaster'

But civilians who have managed to escape the wrath of IS also face deteriorating conditions, with little help being offered to the tens of thousands in refugee camps outside the city.

"We have a humanitarian disaster inside Fallujah and another unfolding disaster in the camps," the Norwegian Refugee Council (NRC) said in a statement.

"Thousands fleeing the cross-fire after months of besiegement and near starvation deserve relief and care, but our relief supplies will soon be exhausted," NRC chief Jan Egeland said.

As the situation worsens, US-backed Iraqi forces continue to battle the Islamic State group which has held the city in its grip since January 2014.

However, progress has been slow due to IS' systematic use of civilians as human shields.

"Make no mistake: There is absolutely nothing safe for civilians fleeing Fallujah. No safe exits, no safe passage, no safe-haven without risking their lives," Egeland said.

"They risk being shot at, killed by explosive devices on the roads, or drowning while crossing the river."

On Monday, the UN revealed an estimated 7,000 civilians from the war-torn city escaped the intense fighting through a safe passage established by the Iraqi army.

The mass migration out of Fallujah exerted pressure on eight UN camps erected outside of the city, with reports suggesting shelters were now full and "overwhelmed".

An estimated 24,000 have fled IS-held areas since a wide-ranging offensive was launched to battle the militant group in May - but refugee organisations insist at least 50,000 still remain within the city limits.

Iraqi forces launched a broad offensive to retake Fallujah last month - one of the two major cities still under IS-control - following victories in other parts of the country.