The Iraqi army has secured the first safe exit route for civilians to escape the Islamic State group's stronghold of Fallujah in Iraq, and a Norwegian aid group says thousands of people have already used it to flee.

Key points: 4,000 civilians reportedly escape from Fallujah amid assault against IS

4,000 civilians reportedly escape from Fallujah amid assault against IS A multi-pronged attack has been launched against IS in Iraq and Syria

A multi-pronged attack has been launched against IS in Iraq and Syria At least 30 people are reported killed in air strikes amid Syrian assault

Iraqi security forces launched a major operation last month to recapture the militants' bastion of Fallujah, an hour's drive from Baghdad, but Prime Minister Haider al-Abadi said troops were delaying advances to protect civilians.

Tens of thousands of people have been trapped in Fallujah since it was captured by the Islamic State (IS) group, threatened with death by the militants if they fled.

Those who managed to escape said they walked for days to avoid sniper fire and explosive devices planted by the IS group.

Displaced Iraqis who were evacuated from their villages south of Fallujah. ( AFP: Moadh Al-Dulaimi )

Aid agencies on the ground said they were completely overwhelmed by the numbers of people fleeing, and urgent deliveries of supplies were needed to cope with the influx.

The United Nations fears for the fate of up to 90,000 people believed trapped inside Fallujah with little food or water.

The new exit route, known as al-Salam (Peace) Junction, was secured south-west of Fallujah on Saturday (local time), said Joint Operation Command spokesman Brigadier-General Yahya Rasool.

"There were exit routes previously, but this is the first to be completely secured, and it's relatively safe," the Brigadier-General said.

About 4,000 people had fled the city over the past 24 hours through the al-Salam Junction, said Karl Schembri, a spokesman in Iraq for the Norwegian Refugee Council (NRC), which has been assisting people who escape the city.

"We expect thousands more to be able to leave in the coming days," he said.

The NRC said humanitarian groups needed a extra $US10 million to provide water, food and hygiene kits to 75,000 displaced Iraqis over the next six months.

"We are also extremely worried that the current funding is running out; we are overwhelmed by the needs created by this crisis and international donors have to step up their funding," said NRC country director in Iraq, Nasr Muflahi.

"This is a moment of truth for wealthier nations to stand by Iraqis who have been facing chronic displacement and untold suffering."

Dozens killed amid Syrian assault against IS

While it pressed on with its offensive in Fallujah, the army also launched a fresh advance in the direction of the northern city of Mosul, the IS group's de facto Iraqi capital, under cover of airstrikes from a US-led coalition.

The assaults by the Iraqi army are taking place at the same time as advances against the militant group by US-backed fighters and Russian-backed Syrian government forces in Syria, at the opposite end of the militants' self-proclaimed caliphate.

Syrian Civil Defence members gather at a site following air strikes on Idlib, Syria. ( AFP: Omar Haj Kadour )

Hundreds of civilians escaped the IS stronghold of Manbij in nearby Aleppo province on Sunday (local time), helped by a US-backed Kurdish-Arab alliance surrounding the town.

Fighting on a range of fronts in both Iraq and Syria in recent weeks amounts to some of the biggest pressure on the militants since they swept across much of Iraq and Syria in 2014 and declared their rule over all Muslims from territory that is home to millions of people.

Amid the Syrian assault, air strikes blamed on either Syrian regime forces or Russian jets have reportedly killed 30 people in rebel-held areas in the north-western Idlib province.

Horrific pictures on social media showed the burnt corpse of a child, purportedly killed in the bombing of a busy market in Idlib city.

In another airstrike in Idlib province, four children from the same family were reportedly killed.

The UK-based Syrian Observatory for Human Rights said regime and allied Russian warplanes were flying in the area but they did not know yet which planes had carried out the strikes.

Meanwhile on the outskirts of Damascus, activists told the ABC that 38-barrel bombs were dropped on the besieged city of Daraya on Sunday.

ABC/wires