Iraq's elite counterterrorism forces pushed deeper into Islamic State-held Fallujah on Wednesday, more than two weeks after the operation to retake the city from the militant group began, a senior military official said.

After securing the southern edge of the city Sunday, Iraqi special forces have entered the Shuhada neighborhood, Maj. Gen. Hadi Zayid Kassar, deputy commander of the counterterrorism forces in Fallujah told The Associated Press.

The operation to retake Fallujah is expected to be one of the most difficult yet: The city in western Iraq's Anbar province is symbolically important to the militant group and has been a bastion of support for anti-government militants since the 2003 U.S.-led invasion toppled Saddam Hussein.

Artillery and rocket fire cleared the way, and a column of black Humvees was seen moving in between the low-rise buildings of Shuhada, a southern neighborhood. After Iraqi forces began their advance, a quick succession of coalition airstrikes followed, filling the sky with dark gray smoke.

Just before the push, Lt. Gen. Abdel Wahab al-Saadi drove to the edge of the territory that Iraqi forces control.

Surrounding buildings have been shredded by artillery fire and the dirt roads running through the mostly agricultural neighborhood have been churned by Iraqi troops' heavily armored vehicles — an indication of the ferocity of the fighting.

The main roads to and from the front line are marked with craters from airstrikes and roadside bombs, with defensive trenches dug by both ISIS and Iraqi forces.

Different Iraqi forces are taking part in the fight for Fallujah, but only Iraq's counterterrorism troops are actually entering the city. Paramilitary troops, made up mainly of Shiite militias, have been given the task of pushing the militants from the outskirts and tightening the siege.

"We expect to face more resistance, especially because we are the only forces entering the city," said Gen. Haider Fadel, one of the commanders of the counterterrorism forces.

"The Daesh are concentrating all their forces in this direction," Fadel said, using an Arabic acronym for the Islamic State group.

Maj. Gen. Gary Volesky, the U.S. commander in Iraq, defended the performance of Iraqi forces in the operation, saying they were playing a larger role than the Shiite militias in leading the isolation of Fallujah.

"The Iraqi security forces have not stalled," Volesky said. "They are continuing to move, they got the isolation done pretty rapidly."

Fallujah is one of the last IS strongholds in Iraq. The Sunni militant group has controlled the city, located about 40 miles west of Baghdad, for more than two years.

Iraqi forces have faced stiff resistance from ISIS in the fight for Fallujah. Extensive use of tunnels, well-trained snipers and roadside bombs slowed the initial push into the city.

After an ISIS blitz across Iraq in summer 2014, the military has slowly won back territory from the militants. But the group still controls patches in Iraq's north and west, as well as the second-largest city of Mosul.