The general running the coalition's ground campaign in Iraq is urging Iraqi forces fighting for Mosul not to "go so fast that they start to give opportunity to the enemy."
"I'm not telling the Iraqis to rush to Mosul. I'm telling them, 'You've got the momentum — sustain the momentum. Continue to put unrelenting pressure on the enemy, and then the enemy is going to break," Major General Gary Volesky told reporters Wednesday via teleconference from Baghdad.
The general said he expected Islamic State fighters to fight with a "full-fledged conventional defense in Mosul" until they lose the city. After that, he said, IS will turn into more of an insurgent force, using unconventional methods to make harassing attacks on Iraqis forces and civilians.
"We are telling Daesh that their leaders are abandoning them. We've seen a movement out of Mosul," Volesky said.
The U.S. has provided intelligence, logistics support, thousands of airstrikes, artillery fire and Apache helicopters to support the fight for Mosul. However, that fight is not the general's sole focus. Volesky said some of his American forces were intentionally placed in other areas of Iraq to prevent any potential Islamic State efforts to shift the Iraqi government's interest to the country's south.
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US General Urges Iraqis 'Not to Rush' Mosul Fight
"We have our advise-and-assist teams with those units who are back in the Euphrates River Valley and those key 'hold' areas to make sure the enemy can't come back and do something that will prevent the Iraqis from focusing on Mosul," he said.
Iraqi Prime Minister Haider al-Abadi seemed to agree with Volesky. On Thursday he said Iraqi forces are "advancing faster than expected" in the fight to retake Mosul.
"The forces are pushing towards the town more quickly than we thought and more quickly than we had programmed in our campaign plan," Abadi said during a conference call with senior officials in Paris.
Smoke rises as people flee their homes during clashes between Iraqi security forces and members of the Islamic State group fleeing Mosul, Iraq, Oct. 18, 2016.
Refugee crisis
Meanwhile, the international charity Save the Children said thousands of people had fled the Mosul area in order to escape the unfolding offensive by Iraqi and Kurdish forces to retake the city from IS.
The aid group said about 5,000 people had arrived in the past 10 days at a refugee camp over the border in Syria, which risks being overwhelmed as more people flee.
"These families arrive with nothing but the clothes on their backs and find almost nothing to help them," said Tarik Kadir, who heads the charity's Mosul response.
A displaced woman who is fleeing from clashes holds her baby in Qayyarah, during an operation to attack Islamic State militants in Mosul, Iraq, Oct. 19, 2016.
Alarm is rising about the prospects for civilians caught in the middle of the battle to retake the Islamic State's last major urban stronghold in Iraq. It's likely to take weeks, if not months.
On Tuesday, Iraqi and Kurdish leaders told Filippo Grandi, the U.N.'s refugee commissioner, that they would do their best to protect civilians. "The protection of the civilians in Mosul cannot be just the responsibility of a few humanitarian organizations," Grandi told reporters in the Kurdistan capital of Irbil.
The United Nations and the government have support materials for up to 400,000 displaced in the fight for Mosul. At least 1 million civilians are estimated to be in the city.
FILE - In this undated file photo released by a militant website, which has been verified and is consistent with other AP reporting, militants of the Islamic State group hold up their weapons and wave flags on their vehicles in a convoy on a road leading to Iraq, while riding in Raqqa, Syria.
Meanwhile, Babatunde Osotimehin, executive director of the U.N. Population Fund, said he was deeply concerned about the rapidly escalating humanitarian crisis in Mosul, and the heightened threat to the health and lives of pregnant women who may be cut off from lifesaving emergency obstetric care.
Osotimehin said that among the 200,000 people likely to be displaced during the initial weeks of military operations in Mosul, an estimated 46,000 are women and girls of reproductive age; about 8,000 are pregnant, and some are about to give birth. He added that lifesaving health services must be maintained and accessible to all who require them.
Unpredictable IS fighters
Militants have fanned out in Mosul, and residents contacted by phone said the center was eerily quiet, with most people hunkered down and waiting for the full storm to hit. U.S.-led coalition and Iraqi warplanes have been avoiding launching airstrikes in residential areas in a bid to reduce civilian casualties.
WATCH: IS destruction in recently-liberated village
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Retreating IS Leaves Destruction in Villages Around Mosul
Residents said they were afraid to venture out and that IS fighters had become more brutal and unpredictable in their behavior.
"There have been two public executions in my neighborhood since Sunday," said Salim, a shopkeeper and father of two. The militants don't mass in large numbers; they move around in small groups, mainly on motorbikes.
The jihadists also are continuing with preparations to defend the city center, blocking roads with mounds of dirt and erecting makeshift barriers. IS fighters bombed two buildings inside Mosul, Kurdish officials reported.
Tuesday, the terror group's propagandists posted online two videos — one seeking to depict a city unaffected by war, using old footage of locals shopping in bustling streets, and another showing armed jihadists patrolling streets and a masked militant threatening America.
"As for you, America, we promise you ... America will be defeated in Iraq and will leave, God willing, again, humiliated, wretched, dragging its tail in defeat," the video posted late Tuesday by the IS-linked Amaq news agency said.
On the battlefield, though, the taunts would seem to be misplaced.
Iraqi army soldiers man a checkpoint as oil wells burn on the outskirts of Qayyarah, Iraq, Oct. 19, 2016.
Popular mobilization force
The terror group has lost more than two dozen villages on the outskirts of Mosul since Iraqi security forces in the south and Kurdish peshmerga fighters in the east launched their long-awaited offensive Monday.
The going has been quicker than Iraqi and U.S. commanders claimed they expected, and morale on the ground reportedly was remaining high. Even so, officials sought to tamp down expectations of a speedy defeat of the terror group as Iraqi and Kurdish forces contend with roadside bombs, snipers, suicide bombers, and hit-and-run attacks by the extremists.
This U.N. map shows expected paths of escape from Mosul
U.S. officials have stressed that the more than 100 embedded American forces will remain with Iraqi and peshmerga counterparts who are involved in coordinating and decision-making, rather than at the front lines of combat. But U.S. Defense Secretary Ash Carter has said U.S. troops are still in harm's way.
Estimates of IS fighters in Mosul range from about 3,000 to 5,000.
The fighting has remained on the outskirts of Mosul. The Kurdish peshmerga have been slowing or pausing their advance to allow units of the Iraqi security forces to leapfrog ahead of them. Iraqi officials say only ISF forces will enter the mainly Sunni Muslim city, but some Shi'ite popular mobilization force (PMF) members insist they, too, will enter the city center.
Volesky stressed Wednesday that the U.S.-led coalition was not supporting the Shi'ite PMF.
VOA U.N. Correspondent Margaret Besheer contributed to this report.