BAGHDAD: The sound of gunfire exchanged between Iraqi forces and the small pockets of ISIS militants rang out across the besieged city of Falluja, American media reported on Sunday.

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.

During a televised address, 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.

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.

Falluja, 40 miles west of Baghdad, has been in the clutches of ISIS since early 2014, part of the group's campaign of terror across Iraq and Syria. The Sunni terror group captured territory in parts of both countries for its so-called caliphate.

The brutal assault to flush out the militants forced thousands of civilians to flee, with ISIS trapping tens of thousands more within the city limits.

Earlier this month, the U.N. refugee agency warned that an estimated 50,000 people are in grave danger, caught in the city-turned-combat zone as the Iraqi military's bombardment intensified.

CNN did not see any civilians on Saturday, but an Iraqi Army officer, Abu Mariam, said that he has spoken with some as they fled, terrified, their faces showed the signs of starvation.

With food shortages and supply lines cut, according to the United Nations, people trapped inside the city have been starving to death.

"Food is scarce," said Um Ahmed, a 40-year-old living in Falluja with her family. "We have mostly been relying on dates for our meals."

Others who refused to fight faced a certain death.

"There are reports of a dramatic increase in the number of executions of men and older boys in Falluja (who are) refusing to fight on behalf of extremist forces," said Leila Jane Nassif, the U.N. agency's assistant representative in Iraq.