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Iraqi forces and allied tribal factions pressed on towards encircling the city of Fallujah on Saturday, making advances on the western and southern fronts despite heavy resistance from Islamic State [IS] militants.

The operation to retake one of IS's most emblematic bastions was progressing well, the head of the Anbar Operations Command told °®Âþµº.

"The army, backed by local tribal forces, has liberated Falahat western Fallujah," Major General Ismail al-Mahalawi said.

"Iraqi forces have advanced one kilometre [0.6 miles] towards Fallujah," he added.

The forces faced resistance fierce resistance by IS militants, tribal leader Abdulrahman al-Halbusi told °®Âþµº.

"But the ground forces were backed by Iraqi air forces and received US-led coalition air support, both targeting IS with airstrikes," Halbusi said.

Three kilometres from city centre

On Friday, Iraqi forces had moved within three kilometres [1.8 miles] of central Fallujah and consolidated positions in the south of the city.

"Daesh [IS] wanted the battle to take place outside the city but we have moved in, and retaken all this area in eight days," operations commander Lieutenant General Abdelwahab al-Saadi told AFP, standing on rooftop overlooking Fallujah's southern neighbourhoods.

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"Our troops are here," he said pointing on his tablet computer to spots along one of the main streets in southern Fallujah, "That's 3.1 kilometres [less than two miles] from the main official building in the centre."

"We'll be there, in the very centre, in days. Days, not weeks," he said.

Plumes of smoke and dust rose up in Fallujah's low and grey skyline as Special Forces carried out controlled detonations of bombs planted by IS and jets struck IS targets.

The operation to retake Fallujah, which lies only 50 kilometres [30 miles] west of Baghdad, was launched on 22-23 May.

The first phase focused on sealing the siege of the city and the counter-terrorism service has been leading a second phase that saw forces break into the urban centre of Fallujah.

Concern over the fate of tens of thousands of civilians has slowed Iraqi forces' advance but the operation was meeting its goals, the operation's commander said.

"More than 500 IS members have already been killed since the start of the operation," al-Saadi told AFP.

"Fallujah is a very symbolic place for IS... but the battle is not different from other ones and when they are trapped, they try to run away just like they did before," he said.

IS fighters have tried to leave the besieged city by blending in with the flow of displaced civilians who are attempting to escape by crossing the Euphrates south of Fallujah.

According to the Norwegian Refugee Council which runs displaced camps in Amriyat al-Fallujah, south of Fallujah, more than 20,000 people have fled the fighting over the past three weeks.

Agencies contributed to this report