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Iraqi forces struggled to seize parts of northern Fallujah from Islamic State [IS] control on Monday, as fierce clashes were reported three days after the government declared the city centre recaptured.

Fallujah remains a scene of battle as Iraqi forces struggle to extend their control of the city.

"Clashes in the northern areas of Fallujah have not stopped for three days," a senior local police officer told °®Âþµº.

"IS militants are still roaming across the city as well as controlling the northern parts," he added.

"The militant group has been carrying out surprise attacks on Iraqi forces which have slowed their advance."

The Islamic State group intensified attacks from their bases in north of the city.

"IS have used their position in northern Fallujah to launch missiles and indiscriminately shell the city," the police officer said. "Snipers have also been deployed against Iraqi forces."

The police officer, who spoke to °®Âþµº on condition of anonymity, said advances by the Iraqi forces have been slow at this stage to minimise the risk of losing soldiers.

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"It will take a long time to clear the city from IS militants, especially since Iraqi forces want to minimise losses in their ranks while doing so," he said, "For them time is not as an important factor as it is to minimise the loss of soldiers during the fighting."

But the slow advance made by Iraqi forces in their push to recapture the north of the city has had a staggering effect on civilians fleeing the fighting.

After declaring Fallujah city centre as liberated, the Norwegian Refugee Council recorded 30,000 people had fled the city.

On Sunday, aid agencies warned they are struggling to cope with the massive influx of displacement coming out of Fallujah.

"Agencies are scrambling to respond to the rapidly evolving situation and we are bracing ourselves for another large exodus in the next few days as we estimate that thousands more people remain trapped in Fallujah," said Bruno Geddo, the representative for the UNHCR in Iraq, in a statement on Sunday.

Civilian exodus has overwhelmed camps run by the Iraqi government and humanitarian groups, leaving thousands without shelter or proper sanitation, the Norwegian Refugee Council said.

"Right now as we speak there are thousands without any tents, without any shelter, they have slept overnight out in the open," said Karl Schembri with the Norwegian Refugee Council.

The humanitarian situation in Anbar province following the Fallujah operation is potentially "catastrophic," he added.

Up to 84,000 people had been forced to leave their homes since the start of the government offensive against the IS bastion nearly a month ago.