A senior Iraqi general has announced on state TV that the battle for Falluja is over as Iraqi troops retook the final ISIS holdout in the city.

By Euan McKirdy and Hamdi Alkhshali, CNN

Lt. General Abdul Wahab al-Saadi said the city was liberated Sunday after recapturing the neighborhood of al-Jolan from ISIS. It was the last area of Falluja that ISIS had controlled, he said while standing in the neighborhood.

Over 1,800 ISIS militants were killed during the military operations by the Iraqi forces to recapture the city and villages surrounding it, al-Saadi, commander of the liberation of Falluja operations, told al-Iraqiya TV.

"We announce from the central al-Jolan neighborhood that this neighborhood has been cleaned by the counterterrorism and federal police forces," he said. "From here we announce to Iraqi people that the battle of Falluja is over."

CNN cannot independently verify all fighting in every area of Falluja has ended.

Civilians suffering

Refugees who had escaped ISIS find themselves languishing in hastily-constructed refugee camps where even the basic amenities are lacking.

"All I want is a tent," one man told CNN. "I asked God, I asked the government: give me a tent to protect my family."

Open cesspits and a solitary toilet for over 3,000 people are visible testaments to the wretched conditions these people are enduring. Relief workers and aid groups are doing what they can, but demand far exceeds supply, says Karl Schembri from the Norwegian Refugee Council.

"We escaped from the tyranny of ISIS," one woman said. "Now we need the Iraqi government to stand with us."

Despite the complete recapture of Falluja, aid groups stressed that safety is still a concern and urged displaced families not to return home.

"We just do not know which areas are safe and which aren't; we need a thorough de-mining of civilian areas and safety assessments before civilians are given the option to go back," said Nasr Muflahi, the Norwegian Refugee Council's Country Director in Iraq.

"While conditions in camps remain extremely dire, we are not in a position to ensure people will get basic supplies and services in Fallujah," Muflahi added.

On the back foot?

ISIS appears to be on the defensive across the Middle East -- from its self-declared capital of Raqqa in Syria to Falluja, a strategically important city just 65 kilometers (40 miles) from the capital, Baghdad.

In a symbolic victory, troops from the Iraqi Federal Police raised the national flag over the Falluja mayor's office Friday. The move came nearly four weeks after the start of a U.S.-backed offensive to liberate the city, the last major ISIS foothold in Iraq's Anbar province.

It's been a fierce campaign, with fighting taking place street by street. And bombs remain, even if most ISIS fighters have been driven from the city.

Many houses are booby-trapped, forcing Iraqi forces to move slowly and methodically to clear improvised explosive devices, or IEDs.

"They don't leave any house without first rigging it with explosives," one counterterrorism member told CNN.

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