Story highlights CNN crews witness fierce fighting near Falluja's city center

Iraqi Government declares the city "liberated" from ISIS

(CNN) The sound of gunfire exchanged between Iraqi forces and the small pockets of ISIS militants rang out across the besieged city of Falluja.

ISIS defenses collapsed as Iraqi special forces made rapid advances into the heart of the city Friday- their fiercest push yet to retake Falluja - but by Saturday morning, the battle waged on.

Troops from the Iraqi Federal Police engage in a battle with ISIS militants in Falluja

During a televised address on Friday, Iraq's Prime Minister Haider al-Abadi said "we promised you the liberation of Falluja and we retook it," the region's governor later declaring on Twitter that Falluja has "returned to the nation."

But, according to a CNN crew who accompanied troops into Falluja on Saturday, the city appeared far from liberated, despite claims to the contrary by the Iraqi government.

#Fallujah is liberated. #DAESH is rapidly collapsing. We must now focus our efforts on a major humanitarian catastrophe still unfolding. — Sohaib Alrawi (@Sohaib_Alrawi) June 17, 2016

In a symbolic victory, troops from the Iraqi Federal Police raised the national flag over the mayor's office Friday, claiming control over the city center, something Iraq hasn't been able to claim in more than two years.

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