Iraqi soldiers talk during a lull in the fighting against Islamic State militants on Nov. 11, 2016, as security forces were pushing through parts of Mosul. The United Nations reported the militants have executed dozens of people in the city for alleged treason. (Odd Andersen/AFP/Getty Images)

Since pushing into Mosul a week ago, Iraqi commanders say their forces have been shaken by some of the most complex fighting they have ever encountered in battles against the Islamic State.

It is a bitter fight: street to street, house to house, with the presence of civilians slowing the advancing forces. Car bombs — the militants’ main weapon — speed out of garages and straight into advancing military convoys.

“If there were no civilians, we’d just burn it all,” said Maj. Gen. Sami al-Aridhi, a counterterrorism commander. He was forced to temporarily pause operations in his sector Monday because too many families were clogging the street. “I couldn’t bomb with artillery or tanks, or heavy weapons. I said, ‘We can’t do anything.’ ”

Mosul is the most populous city held by the militants, with an estimated 1 million people still living there. Iraqi forces have been closing in from the north and south but have broken into the city only on the eastern front, beginning a slow grind through densely populated neighborhoods.

It’s a long, hard slog to the Tigris River that carves through the center of Mosul — and then a whole new battle awaits on the other side. Commanders expressed confidence that they eventually will prevail, but they are less optimistic that they will meet Prime Minister Haider al-Abadi’s pledge to have the city under control by the end of the year.

Militants wait to move between fighting positions until people fill the streets, using their presence as protection from airstrikes.

“They always keep them with them,” Aridhi said. Other officers said the militants occasionally let a flood of people flee as a method of forcing a pause in the fight.

People carrying a white flag and belongings flee fighting as Iraqi soldiers engage Islamic State militants in Mosul on Nov. 11, 2016. (Odd Andersen/AFP/Getty Images)

At their base on the outskirts of the city, Iraqi counterterrorism troops call in airstrikes where they can, radioing to report militant positions and suicide bombers. Two French advisers sit nearby watching surveillance feeds of the city’s streets.

The voice of a field commander crackled through the radio. “These civilians are making me tired,” he said. “They are coming from everywhere. We don’t know if they are fighters or civilians. They are carrying bags — we don’t know what’s inside.”

Col. Arkan Fadhil calls in airstrikes from the U.S.-led coalition, but they are less forthcoming than in previous battles because of the presence of families, and are used only to defend Iraqi forces rather than backing them when they attack.

Just a few Islamic State militants hidden in populated areas can cause tremendous chaos. Seven would-be suicide bombers were arrested as counterterrorism troops cleared the last corners of the Zahra neighborhood of Mosul on Thursday, nearly a week after they had entered it.

It was one of six neighborhoods that the elite units stormed Nov. 4, on a day that was initially trumpeted as a success before it became clear that their early gains were not sustainable. After pushing forward with relatively little resistance, the forces were ambushed and cut off. A CNN team was trapped with them and surrounded for more than 24 hours after their convoy was attacked.

Iraqi soldiers move in formation through an alley on the outskirts of Mosul on Nov. 4, 2016. (Marko Drobnjakovic/AP)

“They fired rockets from over there,” Ghalib al-Lahaibi said from the roof of his home in Mosul’s Samah neighborhood, pointing deeper inside the city. From there, the sound of heavy gunfire and explosions still rang out five days later, as the counterterrorism troops fought to expand their foothold.

Lahaibi’s family hid inside as groups of Islamic State militants passed by carrying rocket­propelled grenades. Stray bullets gouged holes in his living-room walls.

The house shook as a pickup truck full of explosives rammed into a convoy of Iraqi security forces nearby, scattering debris and body parts onto the street. Iraqi forces have little time to react, let alone call in airstrikes.

“You’ve got less than 10 meters to engage, so you shoot and cross your fingers,” said Fadhil, the colonel.

The Iraqi military does not release casualty numbers, but the losses in the Nov. 4 battle appear to have been particularly heavy.

“I’ve lost count,” Jorge Calzadilla, a volunteer with a Slovak medical organization, said about the number of military wounded. One night his group received nine dead soldiers at once. “It was just a truckload of mangled bodies,” he said.

The plan that day, according to Fadhil, was to “rock their defensive line at multiple points.”

A boy reacts as Iraqi soldiers help him walk from the front line during a battle with the Islamic State in eastern Mosul on Nov. 4, 2016. (Zohra Bensemra/Reuters)

Low-ranking officers in the field made some mistakes, he said, such as pushing forward without waiting for other units or without properly clearing and securing areas, later getting ambushed and becoming surrounded and trapped. Since the pitched battles of Nov. 4, the counterterrorism troops have adjusted their pace.

Aridhi said they have had to slow down as they wait for other fronts to advance on the city. Whether they can fight inside when they reach it also remains to be seen. In the battle for the city of Ramadi, the elite counterterrorism troops ended up leading the entire fight after police and army forces struggled to move forward in their sectors.

Restrictions in the use of airstrikes also slow their advance.

But on Tuesday morning, more than half a dozen rockets roared overhead into the Mosul neighborhood of Tahrir.

Officers identified them as TOS-1 short-range missiles, which unleash a blast of pressure over an area of several hundred square meters, devastating anything in their wake. The officers said they had been informed that there were no civilians in the target area.

“We only use these missiles in empty areas,” Aridhi said. “We don’t use them in places with families in it.” They sometimes are used when Iraqi forces are under heavy direct fire, he said, because it is faster than sending coordinates to the coalition.

As the battle drags on, thousands of civilians trapped inside Mosul are risking their lives to escape, making their way across the battlefield in small groups carrying white flags.

They describe the defenses that the Islamic State has built in its neighborhoods — tunnels, concrete barriers, car bombs.

“They are in the apartments,” said one 64-year-old woman as she reached the security forces. “They aren’t allowing anyone to leave. They have car bombs there.”

“In the apartments and where else?” asked an Iraqi counterterrorism officer as the woman was handed water and food.

“All of Mosul,” she replied.

Mustafa Salim contributed to this report.