Smoke rises from ISIS positions following a U.S.-led coalition airstrike as Iraqi Security forces advance their position in Ramadi, Iraq, Tuesday, Dec. 22, 2015.

Iraqi forces on Tuesday reported progress in the military operation to retake the city of Ramadi from ISIS, saying they made the most significant incursion into the city since it fell to the militants in May.

Losing Ramadi — the capital of sprawling western Anbar province and Iraq’s Sunni heartland — was a major blow to the Iraqi government. It was the government’s biggest defeat since ISIS militants swept through areas in the country’s north and west, including Iraq’s second-largest city of Mosul, in the summer of 2014.

Iraqi forces announced a counteroffensive shortly afterward Mosul fell but progress has been sluggish and clawing territory back from ISIS has proven more difficult than expected.

Col. Steve Warren, a spokesman for the U.S. military in Baghdad, said there are 250 to 350 Islamic State fighters in Ramadi, as well as several hundred outside the city on the northern and western perimeter.

“I think the fall of Ramadi is inevitable,” Warren told Pentagon reporters. “But that said, it’s going to be a tough fight … it’s gonna take some time.”

He said American military advisers remained outside the city at al-Taqaddum, a desert air base that is serving as a training site. It was a U.S. military hub during the 2003-2011 war.

Iraqi spokesman Sabah al-Numan said troops crossed the Euphrates River north of the city and its Warar tributary to the west and pushed into downtown Ramadi.

From the south, troops led by the counter-terrorism agency made progress in the Dubbat and Aramil neighborhoods, about 3 kilometers (less than 2 miles) from the city center, Gen. Ismail al-Mahallawi, the head of operations in Anbar province, told AP.

Sporadic clashes broke out and advancing Iraqi forces were forced to remove roadside bombs planted by the extremists, al-Numan added.

On Tuesday, the Dubbat neighborhood saw heavy fighting, with one soldier killed and 14 wounded, said an official in the Anbar operations room, speaking on condition of anonymity because he was not authorized to brief the media.

Warren said U.S. officials found a pamphlet in Fallujah that was distributed to ISIS fighters, calling on them to disguise themselves as Iraqi security forces and then film themselves committing atrocities, such as killing and torturing civilians and blowing up mosques.

According to a copy of the document distributed to reporters, it said the video clips should be distributed to television outlets “to depict the conflict as if it is a sectarian war.” It was signed by a security and military official named Abou Hajer al-Issawi and dated early October.

Warren said he believed the document is legitimate, but so far there were no reports of ISIS fighters posing as Iraqi forces.

Al-Numan said no paramilitary forces — a reference to pro-government Shiite militias whose actions have raised concerns in Sunni territory — were taking part in the operation. The Iraqi air force and the U.S.-led international coalition were providing air support to troops on ground and bombing ISIS targets, he said.

Since overrunning Ramadi, just 130 kilometers (80 miles) west of Baghdad, the Islamic State group has destroyed all the bridges around the city. It also demolished the Anbar operations command and fanned out into the city’s residential areas to set up less conspicuous centers of command.

As the military operation continues, Ramadi’s civilian population — estimated to be between 4,000 and 10,000 — remains mostly trapped inside the city. Iraqi officials say they believe civilians will be able to get out, but coalition officials report that so far they have only witnessed small groups doing so.

Warren said Iraqi forces had dropped leaflets telling residents what routes to use to escape.

Ramadi, like the rest of Anbar province, is overwhelmingly Sunni Muslim, the minority community that complains of discrimination by the Shiite-led government in Baghdad. Some Sunnis in other parts of Anbar and in northern Iraq welcomed ISIS rule, at least initially.

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