Iraqi Prime Minister Haider al-Abadi’s decision to engage the Islamic State group in Fallujah is about more than defeating the terrorist network. It’s about more than establishing safety in Baghdad, and it’s even about more than securing his own political future.

His abrupt departure from America’s script for the war against the Islamic State group, which prioritizes above all else the liberation of Iraq’s second-largest city, Mosul, shows the strength of the other major international influence in Iraq, and its sway on Baghdad.

Iran has reportedly been pressuring Abadi for weeks, if not months, to prioritize Fallujah. But now domestic tensions in Baghdad and disunity among the world powers that have involved themselves in the conflict have cleared the way for the Islamic republic to have more potency than the U.S., Russia, Turkey or any other world power involved in the conflict.

"Tehran has more influence on Abadi's focus, whether on Fallujah or anywhere else, than Moscow, Washington and Ankara combined," says a former U.S. combat commander with extensive experience working with Iraq's senior leaders. "The political disarray in Baghdad, the strangely wandering American political strategy, and the opaque rationale for what American forces we will commit to what tasks in the worst form of gradual escalation, combine to leave decisions open to a host of inputs from military and civilian policy makers from Baghdad to Tehran, before even considering the enemy's vote."

Iraqi mourners carry the coffins of men who were killed fighting alongside Iraq government forces to retake to city of Fallujah from jihadists of the Islamic State group, on June 1 in the Shiite holy city of Najaf. Haidar Hamdani/AFP/Getty Images

The U.S. has spent the week since Abadi announced his new battlefield priorities downplaying the sudden shift, despite reports that the Iraqis provided only scant notice of the campaign to their American military counterparts. Reports have also emerged that U.S. officials privately don’t agree and are concerned about what opening a new front might mean for the overall success of the war if Iraqi forces get bogged down in a protracted battle.

It became immediately clear this week the fight would not mirror previous liberations of some Iraqi towns where disenfranchised Islamic State group presence almost immediately fled. As Pentagon officials point out, Fallujah serves as the extremist network’s last haven in Iraq’s massive Anbar province, and they won’t withdraw easily.

Iraqi forces began capturing villages on the outskirts of Fallujah soon after the fighting began on Monday but have since been met with fierce resistance from the extremist group’s fighters.

“They intend to put up a fight for it, and we definitely have seen intense fighting for those two days,” Pentagon spokesman Navy Capt. Jeff Davis said Tuesday.

After acknowledging before the effort began that Fallujah offers no tactical benefit in recapturing Mosul, U.S. officials have since publicly backed the new campaign and minimized inconsistencies with the larger strategy. Defense Secretary Ash Carter said last week “we are obviously supportive of this operation” and that the U.S. was very much aware of Iraq’s intentions to shift toward Fallujah, despite claims to the contrary from defense officials who spoke to U.S. News.

Marine Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, insisted the Iraqi military could continue preparing for the Mosul operation and simultaneously pursue a detour in Fallujah. Army Col. Steve Warren, speaking from the coalition’s headquarters in Baghdad’s Green Zone on Friday, confirmed that the need to retake Fallujah is driven by “political calculus for the civilian leadership of Iraq” and said success there would ease political pressure on Baghdad before refocusing on Mosul.

That pressure, however, is intense. Shiite protesters loyal to powerful cleric and militia leader Muqtada al-Sadr have stormed the central Green Zone where the Iraqi government and most foreign embassies are based. Outraged by a lack of reform, protesters in April capped months of popular street demonstrations by occupying and ultimately ransacking the parliament building amid fears the government could collapse.

“We often tend to underestimate the degree of threats to Abadi, particularly from other Shiites,” says Stephen Biddle, formerly an adviser to Gens. Stanley McChrystal and David Petraeus who is now with the Council on Foreign Relations. “For most governments like Iraq, internal threats loom larger than external threats, and you can’t just ignore them and treat them as electoral noise. Because that’s how you get killed in a coup d’etat.”

Underscoring concerns that the political instability could hamper the fight against the extremists, the Islamic State group in recent weeks has staged a series of car bombs and suicide attacks in Shiite neighborhoods that marked the group’s return to the terror tactics of its roots, as al-Qaida in Iraq, and exacerbated sectarian tensions.

The long-stalled Mosul operation optimistically appears months away, so targeting Fallujah provides a temporary quick-fix for Abadi politically, using the urgency of the campaign to prove to Iraqis he’s acting to keep them safe. Successfully liberating Fallujah, which is predominantly Sunni, could also earn Abadi some good faith among that constituency nationwide.

Pro-government forces fighters celebrate in the al-Sejar village, in Iraq's Anbar province, on May 27, as they take part in a major assault to retake the city of Fallujah, from the Islamic State group. Ahmed Al-Rubaye/AFP/Getty Images

But some say that, tactically, his attention is likely misplaced. Fallujah, about 40 miles west of Baghdad, is indeed an Islamic State group haven and source of much of its bomb-making capabilities. However, most of the recent attacks on Baghdad have originated from the north, not the west as would be the case if they came from Fallujah, according to the Institute for the Study of War, which regularly analyzes battle rhythms in Iraq.

Other forces are also at play behind the decision, including influences from Tehran that would like the Shiite majority in Iraq’s government to protect Baghdad from what it sees as the threat posed by the proximity of Sunni extremists, like the Islamic State group, while also solidifying its hold on power.

“Iran does not see a government of Iraq that has a Sunni presence in it,” says Scott Mann, who retired as a lieutenant colonel after 18 years as a U.S. Army Special Forces officer with deployments to Iraq and Afghanistan. “This is a way to further divide those ethnicities, between Persians and Arabs, and between Sunni and Shiite, and create a more polarized environment around that conflict.

“They know it, and they’re going to seize any opportunity they can to do that. And ISIS is going to do exactly the opposite. They’re going to create those situations, because they know how Iran is going to play it.”

The overwhelmingly Sunni Muslim city of Fallujah has long been associated with combat in Iraq. It served as a headquarters for al-Qaida in Iraq during the last war and witnessed some of the most gruesome fighting, as U.S. forces in two separate campaigns in 2004 engaged in bloody, door-to-door combat to clear the town of the extremist presence.

Complicating the campaign, the Iraqi government has had to rely on overwhelmingly Shiite Muslim militia forces, known as the Popular Mobilization Forces, in part due to the the U.S.-led coalition’s limitations on providing ground forces, which leaves Baghdad with few other options for the sheer numbers of fighters it needs. These forces are supposed to remain outside the city, where they help prevent extremists’ lines of escape or reinforcement.

Pictures emerged last week of Iranian Revolutionary Guards Corps’ Qassem Soleimani’s meeting with leaders from the local Shiite militias, one of the first times he had appeared in public media since his visit to Aleppo, Syria – another central focus of Iran’s fight against enemy forces in the region. That the shadowy Quds Force commander would publicize his whereabouts further emphasizes the degree to which Iran now prioritizes Fallujah.

Iranian proxy forces, like some of the militias, are a critical component to any chance of success in defeating the Islamic State group. They have contributed to most of the fighting to secure the area around Fallujah, particularly to the north, clearing the way for Baghdad’s announcement late Monday that its U.S.-trained counterterrorism commandos had begun the arduous work of actually entering the city to clear it of the Islamic State group presence. This use of various kinds of military forces has produced a winning combination in the past, like for the liberation of Ramadi. But now it faces its most serious challenge as the few hundred Islamic State group fighters in Fallujah dig in and and use the estimated 50,000 local residents held there as human shields.

The U.S. military argues none of the conventional forces used for the Fallujah campaign would be needed in Mosul. Most experts agree, but that doesn’t mean the sudden detour won’t affect America’s fundamental plans for the battlespace.

“Operations like this chew through resources,” says Patrick Martin, research analyst for Iraq with the Institute for the Study of War. “It’s just going to delay everything.”

He cites reports that the U.S.-trained Counter Terrorism Service – considered the most effective Iraqi fighting force on the ground – has grown exhausted by the continuous demand for troops to lead the way in clearing Islamic State group positions.

And fundamental questions about the future of Fallujah remain, Martin says, particularly following widespread concerns that the Shiite militias wish to exact revenge on Sunni populations for their perceived complicity toward the Islamic State group – a key reason why the U.S. refuses to provide air support to ground operations involving the militias. Shiite militias also have reportedly prevented Sunnis from returning to homes they helped liberate.

“We shouldn’t kid ourselves,” Martin says. “This is what pushes the Mosul operation into delaying it indefinitely, because there are still other questions that haven’t been answered yet.”

All sides agree that liberating Fallujah is simply a matter of time. The effect, though, of an Iranian sponsored victory may only further complicate the total war against the Islamic State group.

The heavy presence of Shiite militia encircling Fallujah provide prime fodder for the extremist network to convince their fellow Sunni Muslims that the Iraqi government is beholden to Iran and has no intention of including them among the ruling classes.

“All they have to say is, ‘Look who’s coming. This is your government that is allowing this to happen, backed by the American Air Force. Only we can help you.’ And they do this brilliantly,” says Mann, the former special forces lieutenant colonel.

“In the short term, will it be effective? Probably. It will force ISIS to go to ground. It may kill some and displace some of them,” Mann says. “In my assessment, this is nothing more than mowing the grass.”