The offensive launched this week by Iraqi government forces to retake the city of Fallujah from ISIS militants represents the most important test so far of Iraqi Prime Minister Haider al-Abadi's leadership as well as of U.S. military strategy in the region. Driving ISIS out of Fallujah, where U.S. forces waged a fierce battle in 2004 against al-Qaida, would represent a huge victory for the Iraqi government because the city was one of the first major urban areas in Iraq to fall to the extremists in 2014. It would also vindicate President Barack Obama's strategy of supporting local fighters with airstrikes, intelligence and logistical support while avoiding putting U.S. boots on the ground.

On Sunday, Iraqi special forces backed by U.S. airstrikes and Shiite militias finished surrounding the city where some 50,000 civilians are thought be trapped by an estimated 400 to 500 ISIS militants. Mr. al-Abadi has vowed to eject the ISIS fighters in short order, but the militants have had two years to dig in and strengthen the city's defenses with improvised explosive devices, sniper nests and a network of underground bunkers and tunnels, fortifications that in recent days have slowed the government advance.

The U.S. commander in Iraq, Lt. Gen. Sean MacFarland, has warned that it's too soon to say how long the battle will take because many civilians in the Sunni stronghold, distrustful of the Iraq's Shiite-dominated government in Baghdad and fearful of the Iranian-backed Shiite militias supporting it, may ultimately decide to throw in their lot with ISIS. One reason many Fallujah residents were receptive to ISIS' takeover two years ago is that they had become deeply disillusioned by former Prime Minister Nouri al-Maliki's policies, which marginalized their interests in the central government. That is a political problem Mr. al-Abadi must find a way to overcome if his government is to successfully reassert its control of the city over the long run.

Meanwhile, aid organizations have warned of a looming humanitarian crisis among the city's 50,000 civilian residents, including as many as 20,000 children, whose departure the militants have blocked. Reports suggest that ISIS may intend to use civilians as human shields; reportedly the group has killed whole families for attempting to flee the city even as overall conditions for residents have steadily deteriorated in recent months because of a government siege that has intensified shortages of food and medicine. The crisis has left the government scrambling to deal with an anticipated exodus of residents from the city.

The government also must try to avoid a repeat of its December 2015 campaign to retake the city of Ramadi, which was occupied by ISIS for about six months last year. While government forces eventually succeeded in ejecting the militants, their victory came at the price of destroying large parts of the historic city, which has suffered more damage than any urban area in Iraq. Government forces still haven't cleared hundreds of bombs and booby traps left behind by ISIS fighters, and they continue to uncover mass graves of civilians, including those killed by Iraq's Shiite militia forces, who have been accused of committing atrocities against civilians in majority Sunni towns and cities.

America never had a strong partnership with former Prime Minister al-Maliki, whose two terms in office alienated the country's Sunni minority and stoked the sectarian resentments that ISIS exploited against his government in Baghdad. Whether Mr. al-Abadi will be able to unify the country and heal those deep divisions remains to be seen, but without a political reconciliation with the Sunni minority that was disenfranchised by the 2003 U.S. invasion that led to the fall of former dictator Saddam Hussein, it's difficult to see how ISIS' appeal to disgruntled Sunnis will diminish in Fallujah — or in Mosul, which U.S. and Iraqi officials hope to retake next. ISIS took control of Mosul in June 2014.

The weaknesses of Iraq's political process will be the determining factor in whether a U.S. strategy that avoids putting American troops on the ground can stop the cycle by addressing the fundamental needs and concerns of the city's Sunni residents. In the coming months Fallujah, and eventually Mosul, will put that question to the test.