The Iraqi government is putting the ISIS-controlled city of Fallujah as next on its target list.

That’s not because of increasingly dire reports that the citizens of Fallujah are suffering from starvation and torture under ISIS’s cruel grip. Nor do Iraqi officials see the city as key to dislodging ISIS from its Iraqi stronghold, Mosul.

Rather, Iraqi officials have told their American counterparts that they suspect the restive Sunni-dominated city is sending jihadists to attack Baghdad, the Shiite-dominated capital. In the last week, there have been multiple daily bombings in Baghdad that have killed more than 200 people and wounded hundreds more. On Tuesday alone, a combination of suicide attacks and car bombings took the lives of nearly 70 people; ISIS claimed responsibility for some of those bombings.

In other words: While all eyes were on Baghdad and the deadliest spate of bombings to strike the capital in years, the Iraqi government was quietly pointing its finger at Fallujah.

Such accusations toward Fallujah, arguably, is precisely what ISIS wanted its bombings to incite, a return to the kind of sectarianism that has, in the past, threatened to tear the state apart—and was supposed to dissipate under Prime Minister Haider al Abadi.

With each bombing, residents of the Shiite-dominated Baghdad have looked at the Sunni-dominated Fallujah with increased suspicion. And the Sunnis trapped under ISIS control in Fallujah believe their Shiite-led government is making their torturous situation worse.

In recent weeks, the Iraqi government has placed parts of three of its divisions—the 1st, 6th, and 7th—around the city. Seven brigades of approximately 1,000 to 1,500 fighters are now committed to this task. And American officials believe the government “wants to be finished” with Fallujah and rid it of ISIS next, as one U.S. defense official explained.

“They’ve got [Fallujah] surrounded. They are pressuring it. But they haven’t been able to make a real move in there to start clearing it yet,” Army Col. Steven Warren, a spokesman for the U.S. effort in Iraq and Syria, told reporters Friday.

But unlike their Iraqi counterparts, American officials are not convinced that Fallujah is the source of the multiple daily attacks on Baghdad. “There is nothing to support that,” a second U.S. defense official explained.

And even if Fallujah is ISIS freed, Iraq won’t be. The security around Baghdad is so bad right now that ISIS could just drive down from Mosul, 170 miles to the north.

Perhaps most important, Fallujah has been under ISIS control for more than two years, longer than any other Iraqi city, making it among the most difficult to dislodge from ISIS’s grip.

The push to launch an Iraqi ground campaign, backed by U.S.-led coalition airstrikes, has created friction between American and Iraqi officials, two defense U.S. officials told The Daily Beast. American military advisers believe that the Iraqi government’s focus should be on Mosul, not Fallujah.

While wanting to rid Fallujah of ISIS is seemingly a worthy cause, the Iraqi government’s reasons behind it do not portend well for an Iraq trying to reduce the level of sectarianism. Before last week’s bombings, Iraqi officials believed it was up to the people of Fallujah to rid the city of ISIS. Some privately looked at the city with contempt, saying they didn’t trust anyone from there.

And when stories emerged of mass starvation in Fallujah by ISIS—forcing some to reportedly eat grass to survive—the Iraqi government was silent. That lack of response only stoked sectarian feelings by the people of Fallujah toward their government.

Mark Alsalih, a Sunni lobbyist and activist who speaks with tribal sheikhs in the region, blamed Shiite militias for surrounding the city and preventing food and supplies from entering. ISIS fighters who have occupied have also refused to let residents leave, he said.

“These militias are not allowing any food shipments or medicines into the city and the people of Fallujah—mostly poor folks that were unable to pay ransoms to ISIS to let them out early on—are stuck there,” Alsalih told The Daily Beast. “This has been going on for months and the people are eating grass to survive—there is famine everywhere.”

Human Rights Watch reported last month that government forces cut off supply routes into Fallujah after taking back the nearby city of Ramadi from ISIS last year, leaving the city effectively shut off from the outside world. Many fled, and now tens of thousands of the city’s earlier original population of more than 300,000 remain, the group says.

Sources inside Fallujah that told human-rights monitors of widespread starvation as well as food price spikes. A 50-kilogram sack of flour was selling for $750 and a bag of sugar cost $500, Human Rights Watch found, whereas in Baghdad, the same items cost $15 and $40.

Human rights groups have also reported that ISIS terrorists who control the city have murdered residents who try to escape. Alsalih said that some stranded civilians have lost all hope. Recently, he said, a woman whose husband ISIS had executed tied herself and her three children together with rope and jumped off a bridge into the Euphrates River, where they drowned.

“ISIS no longer allows the city’s residents to cross the old bridge because of all the people using it to commit suicide—out of starvation and mass hysteria due to their horrific living conditions,” Alsalih said. He added that his contacts in the area “are convinced that the U.S. will not do anything to help them,” because Fallujah was once a hotbed of Iraqi resistance members who fought U.S. forces prior to their withdrawal from Iraq in 2011.

Despite such troubling reports, it was not until recent weeks that the Iraqi officials said it was time to go into Fallujah. The city, rather than part of a monolithic Iraq, is relevant only in proportion to the threat it poses to the capital, it appears.

But there are particular challenges to taking on Fallujah. In three weeks, Iraq and the Muslim world will mark the Muslim holy month of Ramadan, which is a time of rest, reflection and daylong fasting. Following that, Iraq will be unbearably hot for long-term fighting until at least late September.

Even during the days of Saddam Hussein, Fallujah was considered a restive city. Within weeks of their arrival in 2003, U.S. troops found themselves at odds with its residents. A year later, there were two major U.S.-led battles there. It was not until the surge of 2007, which began in Ramadi and brought the U.S. and Iraqi forces together to combat what was then al Qaeda, that a détente emerged between the U.S. and the residents of Fallujah.

Regardless of the Iraqi calls to move in on Fallujah, there is nothing imminent, U.S. officials said. The result, at least in the short term, is both Iraqi and U.S. officials are bracing for more attacks like those that struck Baghdad on Tuesday—and potentially more sectarian tension.