IRBIL, Iraq — Iraqi forces resumed their offensive against the Islamic State in Mosul on Sunday after a weekslong pause, aiming to capture the militant-controlled western half of the city, where the tight, impassable streets and teeming neighborhoods will pose a formidable challenge to the advancing fighters.

Prime Minister Haider al-Abadi announced the offensive in a televised address early Sunday, calling it “a dawn of victories.” As he spoke, units from Iraq’s army, federal police and state-sanctioned militias approached Mosul from the south and west. By day’s end, they had captured a dozen mostly vacant villages south of Mosul, along with an electricity station, officials said.

The painless start belied a complicated and arduous battle ahead. Eastern Mosul was captured in January after months of punishing urban combat that left hundreds of civilians dead and elite Iraqi units battered by the stiff militant defenses, including roadside bombs, sniper fire and explosives-laden vehicles.

Iraqi troops will face all that and worse in western Mosul, across the bombed-out bridges on the Tigris River, fighting in a warren of streets too narrow for tanks against Islamist militants who have had months to prepare a deadly welcome. Each passing week of combat poses growing risks to hundreds of thousands of civilians still in the city, facing shortages of food, water, electricity and medicine and all but sequestered in their homes until Iraqi troops arrive.

“Families in western Mosul tell us escape is not an option – if they try to flee, they risk summary execution by ISIS fighters or a gauntlet of sniper fire and land mines,” Maurizio Crivallero, the Iraq country director for Save the Children, the Britain-based charity, said in a statement last week, using an acronym for the Islamic State.

About 350,000 children remain trapped in the city, he said. “The impact of artillery and other explosive weaponry in those narrow, densely populated streets is likely to be more deadly and indiscriminate than anything we have seen in the conflict so far,” he said.

U.S. troops involved in the air campaign said Sunday that there is broad recognition that it will be harder to carry out airstrikes in the western part of the city, citing the way remaining fighters have entrenched themselves as well as the closely settled nature of neighborhoods.

“It’s going to be a full-on cat-and-mouse fight in western Mosul,” said Air Force Lt. Col. August Pfluger, a squadron commander and F-22 Raptor pilot. “We are literally fighting city block by city block, and putting ordnance where the Iraqi ground forces want them.”

The offensive aims to reverse the Islamic State’s stunning advance into cities and towns across Iraq in the summer of 2014, a humiliating defeat for Nouri al-Maliki, Abadi’s predecessor as premier, and a setback that raised concerns about the morale and capabilities of Iraq’s military.

The latest advance on Mosul also comes at a time of rising tension between the Iraqi government and the U.S. over the White House decision to halt immigration from seven Muslim-majority countries, including Iraq.

The Trump administration’s escalating condemnations of Iran, a dominant power in Iraq and a sponsor of Shiite militias fighting alongside Iraqi government units, has also threatened to complicate the efforts against the Islamic State.

Defense Secretary Jim Mattis, speaking Sunday in Abu Dhabi, United Arab Emirates, said that U.S. forces would continue “with the accelerated effort to destroy ISIS.”

In the past few days, the U.S. has stepped up its air sorties over Mosul, to about 30 to 50 a day from about 12 to 20, said Col. Kevin M. Eastland.

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