U.S.-backed Iraqi forces announced Thursday they have retaken one of the Islamic State's remaining strongholds after about 1,000 militants surrendered amid fresh signs the terror group is collapsing and unable to defend its territory.

“They’re giving up,” said Lt. Gen. Paul Funk, who commands the coalition task force fighting the Islamic State in Iraq and Syria. “Their leaders are abandoning them.”

The fall of Hawija in northern Iraq, after two weeks of fighting, is the latest in a string of defeats for the Islamic State, also known as ISIS, and suggests the rank-and-file fighters are demoralized as the group struggles to defend what remains of the territory it seized in 2014.

“The speed at which the enemy gave up surprised me,” Funk told USA TODAY in a phone interview from Baghdad, after Iraqi Prime Minister Haider al-Abadi announced the liberation of Hawija.

Funk said about 1,000 militants surrendered in the past three or four days of fighting in Hawija. The coalition had estimated up to 1,500 militants were defending the city when the offensive began.

In July, Iraq announced that Mosul, the country’s second-largest city, was retaken from ISIS after about nine months of intense fighting. Since that decisive battle, the pace of the Islamic State's decline seems to have quickened.

U.S.-backed forces in Syria have recaptured about three-quarters of Raqqa, the ISIS headquarters, after about four months of fighting in the city.

ISIS' fierce reputation rested partly on the willingness of hardcore militants to fight to the last man, and the militants rarely surrendered.

But many of the fanatical foreign fighters who initially provided the leadership have been killed and those remaining on the battlefield are conscripts, who often lack the will to fight.

“They’re coming out with their hands up, putting their weapons down — full scale surrender,” Funk said. “It’s a growing trend.”

“What we are hearing (from those who surrendered) is, ‘Our leaders have abandoned us, we haven’t been fed, we haven’t been paid,’” Funk said.

Last week ISIS leader, Abu Bakr al-Baghdadi released an audio exhorting his fighters to continue the battle. "I don’t think he's having much of an effect," Funk said. The day after the audio was released, several hundred fighters surrendered.

Fighters who surrendered or are captured are held by Iraqi or Kurdish forces.

ISIS swept into Iraq from Syria in 2014, capturing large swaths of territory. From a mosque in Mosul, al-Baghdadi announced the establishment of the group's so-called caliphate.

Today, as few as 3,000 militants might remain in Iraq in Syria, down from estimates up to 30,000, though officials caution that the numbers aren’t a good measure of the group’s strength.

Terror groups like the Islamic State have proven resilient, regenerating leaders and conscripting or recruiting new waves of fighters.

Coalition officials said the fight is not over, despite the progress. ISIS militants still control a string of towns and villages stretching along the Euphrates River in Iraq and Syria, where they are expected to make a last stand.

"It won't be easy and won't be quick," Funk said.

More:Defeat of ISIS in northern Iraq town marks milestone in campaign to eliminate group

More:Defeat of ISIS in northern Iraq town marks milestone in campaign to eliminate group

More:Islamic State releases purported audio from leader al-Baghdadi