MOSUL, Iraq >> As Iraqi forces pushed Islamic State militants out of Mosul’s eastern neighborhoods this week, hundreds of civilians faced a dilemma: Stay in an area still beset by heavy fighting and surrounded by government troops that many still distrust, or evacuate for the uncertainty of a displacement camp.

The elite special forces entered the Gogjali district Tuesday, touching off an exodus by hundreds of residents, many herding sheep, cows and goats as they fled to the east.

But still more have been told by the troops to stay in their homes as the battle is changing to one of urban combat with the extremists who hold Iraq’s second-largest city. Those civilians who remain have essentially become trapped on the front lines.

As a convoy of armored Iraqi vehicles twisted through narrow dirt roads, a handful of families waved. Some children shouted and smiled at the passing troops, but other residents peeked cautiously from behind garden gates. In the center of the district, a crowd lined up to collect boxes of aid.

One resident at the aid distribution site said the mood in the neighborhood was more tense than exuberant.

“We don’t feel entirely safe, maybe 50 percent,” he said, explaining the edges of the district were still getting shelled heavily by the Islamic State group.

The resident, who asked not to be identified because he still has relatives in Mosul, said he had tried to flee, but Iraqi security forces told him he had to stay in Gogjali.

“Everyone here is trapped in this situation. They’re afraid,” he said.

On Thursday, an explosives-laden vehicle sped out of an IS-controlled area toward the special forces positioned in Gogjali, Brig. Gen. Haider Fadhil said. The troops fired a rocket that blew up the car, killing the attacker.

Fadil also said the militants were using explosives-laden drones, deploying two since the previous night, both of which had been destroyed.

In addition to consolidating territory, rooting out any IS fighters who may have stayed behind and checking for planted explosives left by the militants, the Iraqi troops have to handle those civilians who are fleeing IS-held territory deeper inside Mosul. More than 5,000 people have been evacuated to nearby camps since Wednesday from Gogjali and nearby areas, said Lt. Gen. Talib Shaghati, commander of the Joint Military Operation command.

About 22,000 people have been displaced from Mosul, with about half settled in camps and the rest in host communities, U.N. spokesman Stephane Dujarric said. The U.N. and its humanitarian partners have distributed food, water and medicine to more than 25,000 displaced people and vulnerable residents in Iraq’s newly retaken towns, he said.

Many residents who ventured onto Gogjali’s streets were still dressed as if living under IS rule: women wore the niqab — a black veil covering their face — and men had full beards. One Iraqi soldier in the convoy held up a cellphone and recorded video of the unshaven men — his first glimpse in more than two years of life inside Mosul.

Among Mosul’s residents, there is a deep distrust of Iraqi security forces, a feeling that contributed to the growth in power of the Islamic State group even before it fell to the militants in the summer of 2014.

Under former Prime Minister Nouri al-Maliki, many residents viewed policemen and soldiers who patrolled the streets and manned checkpoints as an occupying force.

A group of top Iraqi soldiers gathered on a rooftop overlooking the Gogjali neighborhood Wednesday and detailed the progress of the offensive that began Oct. 17.

“All of those sections to the west have been cleared,” said Maj. Salam al-Obeidi, pointing across a row of houses and referring to satellite imagery on his tablet computer. The low thuds of IS mortar fire could be heard in the distance along the front.

In the fields below, families holding homemade white flags approached on foot.

“Why are you leaving? We are here to protect you,” said special forces Gen. Sami al-Aridi.

“It’s better for them to stay,” he told reporters. “The weather is getting cold and they have small children with them, and we don’t have any food to give.”

Two of his deputies said the real reason they were told to keep families in place was to screen them for potential IS fighters hiding among civilians, as well as to gather intelligence that could help the Mosul operation. The officers spoke on condition of anonymity because they were not authorized to brief the press.

Adding to the uncertainty among the population were rumors and hearsay.

Hussein Abd al-Aetar said he packed up his family and set out on foot after a rumor spread in his neighborhood that the army was telling families to evacuate.

“They said if we don’t leave, they’ll come at night to force us out,” he said.

A woman in the crowd said she was trying to flee because she feared the airstrikes and street fighting were getting closer while her food supply was almost all gone.

How Iraqi forces handle the humanitarian and security situation in Gogjali amid their offensive will be the first major test of the government’s ability to deal with the civilians still inside Mosul.

Mosul and surrounding villages are home to about 1 million people, and aid groups have warned of a potential humanitarian catastrophe. In past operations to recapture cities from IS, urban areas have been emptied of their inhabitants, but in Mosul, the military is urging civilians to stay in their homes and avoid a massive displacement.

Al-Aridi, the special forces general, told the crowd: “Move to another home, any that you find is empty, but don’t go far. We’ll advance the front line in the coming days.”

But just a few yards (meters) from the homes that troops insisted were safe, other soldiers had gathered around two dead Islamic State fighters.

“They tried to attack us late last night,” said Sgt. Maj. Ali Abbas, also with the special forces. “They had weapons and we tried to arrest them, but they resisted, so we shot them.”