U.S.-backed Iraqi troops continue to fight Islamic State (ISIS/ISIL) jihadists in Fallujah, days after the Baghdad-based government declared the city to be “liberated” from terrorists.

On Friday, Iraq’s Prime Minister Haider al-Abadi proclaimed, “We promised you the liberation of Fallujah and we retook it.”

Fallujah “is liberated,” later tweeted Sohaib Alrawi, the governor of Anbar, Iraq’s largest province, where the city is located.

On Monday, Brett McGurk, President Barack Obama’s special envoy for the U.S.-led coalition against ISIS, congratulated the Anbar governor on Twitter for the Iraqi troops’ “liberation” operations in Fallujah.

However, CNN reported on Saturday that “the city appeared far from liberated, despite claims to the contrary by the Iraqi government.”

The Associated Press (AP) later noted:

Iraqi forces battled Islamic State militants in pockets of Fallujah on Monday, days after the government declared the city’s liberation. Iraqi special forces say they are closing in on the remaining IS strongholds but that their progress has been slowed by snipers hiding in residential buildings.

Brig. Gen. Haider al-Obeidi from the Iraqi special forces predicted that the Islamic State, also known as IS, would be pushed out of Fallujah in the next few days, according to AP.

“IS militants still control the northern Golan neighborhood as well as other scattered pockets, where they are largely surrounded,” reports the news agency.

The jihadist group is fighting to the death, according to various assessments.

Gen. Obeidi estimated that 80 percent of the city was under their control as clashes were ongoing.

Reuters learned from one Iraqi commander, Lt. Gen. Abdul Wahab al-Saidi, that the “U.S.-backed Iraqi forces fighting Islamic State militants in Falluja are advancing toward jihadist strongholds in western districts where they expect the final push to recapture the city will take place.”

“The biggest effort now is on the western axis. If they collapse on the western axis and our forces reach Golan, you won’t hear any more shots inside Falluja,” declared the commander.

According to the United Nations, more than 82,000 residents have fled Fallujah to overwhelmed camps operated by the Iraqi government and 25,000 more are likely in the process of evacuating.

ISIS reportedly shot some of the Iraqis as they were trying to escape, killing many of them. The jihadist group was also accused of using civilians who were trapped in the city as “human shields.”

Fallujah, located about 35 miles from Baghdad, was the first Iraqi city to fall under the control of ISIS, in January 2014.

Backed by Iran-allied Shiite militias and the U.S. military, the Iraqi forces launched the operation to recapture Fallujah in late May.

The Shiite militias were accused of torturing “hundreds” of civilians and have not been participating in recent battles inside the Sunni-majority city of Fallujah.