A member of the Iraqi security forces stands inside a damaged house in the southern entrance of the city of Tikrit on March 29, 2015 during a military operation to retake city from the Islamic State. (Ahmad Al-Rubaye/AFP/Getty Images)

In the makeshift Iraqi army command headquarters for the operation to clear Tikrit, Brig. Gen. Mohammed Ibrahim reads out the coordinates for targets that planes from the U.S.-led coalition are to strike: the local council building, the teacher’s institute, a local mall.

As he speaks, other planes find their mark, and the headquarters, a former chemical engineering building at the city’s university, shudders from the reverberations.

Since U.S. planes joined the battle to retake Tikrit last week, commanders here say the strikes have killed top Islamic State leaders and reduced the capacity of the militants to move. However, the decision to call in strikes is also a gamble — because it has drastically reduced the manpower of pro-government forces.

Some Shiite militiamen have drawn back from the fight to protest U.S. involvement. While that may suit the American commanders, who do not wish to be seen giving air cover to Iranian-backed paramilitary groups, Iraqi officers on the ground are struggling to plug the gap while negotiations take place to persuade the militiamen to return to the battle.

By Sunday, most of the Shiite militiamen formerly based at the university compound had departed, leaving an eerie silence punctuated by mortar fire and the crack of airstrikes.

The headquarters of the Shiite militia Kitaeb Imam Ali, which has been fighting on the front lines with Iraqi special forces, was empty.

“Orders,” explained Maj. Raed Abbas al-Zubaidi, a commander with the militia, over dinner Saturday night before his departure. He would not say where they came from. His men are leaving their positions on the edges of Qadisiyah, just outside the university compound’s perimeter, to move to the town of Baiji, he said.

Their withdrawal gives the regular armed forces a chance to assert themselves in a battle from which they have largely been excluded. But Iraqi commanders are evidently not happy about the extent of the pullback. As a Shiite sheik visited Saturday from southern Iraq, one army commander implored him to persuade militiamen to say.

“Right now we need them, and honestly, they’ve achieved a lot of victories,” said Lt. Gen. Abdulwahab al-Saidi, a commander with Iraq’s special forces who is heading the operation to retake the city. “If we were a complete army, I’d say otherwise.”

The army is reliant on the manpower brought by what has become known in Iraq as the “popular mobilization.” It is a term that originated last summer to describe the tens of thousands of volunteers who answered a religious call to fight, but it has largely come to refer to Shiite militias.

U.S. involvement has brought to the surface rifts between the militiamen and the government, with militia leaders reacting angrily to the coalition strikes in an operation they were leading.

An Iranian commander who was advising the militias here, Maj. Gen. Qasem Soleimani, has returned to Iran, according to official photographs released by the Iranian leadership.

A member of the Iraqi security forces watches clashes, from over a blast wall, in the city of Tikrit on March 28, 2015. (Ahmad Al-Rubaye/AFP/Getty Images)

Brig. Gen. Ghassan Nouraddin, a senior Iraqi army officer, said that politics has complicated military efforts. “We have the problems of the groups fighting in a sectarian way,” he said. “We also have the problem that the state wants to prove itself on the ground.”

Two battalions of soldiers were being sent to the university to replace the retreating militiamen, army commanders said. A group of 54 volunteers from the southern city of Karbala was dispatched to help hold defense lines at the university.

But there are doubts as to whether that is enough to compensate. Commanders declined to say how many troops are actively in combat for the city of Tikrit — but there’s no doubt their numbers are seriously depleted.

U.S. officials have said that there are about 4,000 soldiers and that they outnumber Islamic State militants here by at least 10 to 1. But in operations in Diyala and Jurf al-Sukhar, south of Baghdad, pro-government forces have relied on overwhelming manpower – largely from militiamen — to win the fight. Soldiers lack the experience in street-to-street fighting necessary in Tikrit, some say.

“This is the first time since 1981 that the Iraqi army has fought like this in an urban area,” said Saidi, referring to the bloody battle for the city of Khorramshahr in Iran during the eight-year war between Iran and Iraq.

But Saidi also appreciates the U.S.-led strikes, which he said add precision that the Iraqi air force lacks. “The Iraqi air force pilots are excellent, but not the aircraft,” he said, adding that the first wave of strikes on Tikrit’s former presidential palaces, now occupied by the Islamic State, killed senior leaders.

Highlighting the need for precision was a friendly-fire incident Wednesday. A fresh, gaping hole lies on the road near the army headquarters — created not by enemy fire but by Iraqi planes. One jet dropped five bombs on the compound.

“We ran like we were being bombed by the enemy,” said one technician at the base, who, like others who spoke about the Iraqi air force’s misfire, did not want to be named because of the sensitivity of the subject.

Nouraddin said about 15 people were injured, four seriously.

Earlier that day, Iraq’s defense minister had proudly seen off his pilots at Rasheed air base in Baghdad. Iraq’s fleet consists of five second-hand Sukhoi Su-25 fighter jets, after deals with Russia and Iran. Seven more remain in the hangars but are not functional, according to pilots at the base.

“It is not about the number of planes, but the results they are getting,” Anwar Hamid, the head of Iraq’s air force, said as he saw the pilots off in Baghdad.

Later, as top commanders in the Iraqi army flew up from Baghdad to investigate, Shiite militias who had contended that U.S. coalition planes would bomb them instead of Islamic State militants were furious. Some militiamen left the base immediately in the wake of the strikes. Larger militias — Asaib Ahl al-Haq, the Badr Organization and Kitaeb Hezbollah — have said they’ve stopped fighting but have vowed to remain in positions on other fronts around Tikrit. There were indications that they may be considering rejoining the fight on Sunday night, after a statement from the public mobilizations group that said all its forces were “determined to liberate Tikrit.”

For those left at Tikrit University, that would be welcome news. At night the air fills with the sound of machine-gun and mortar fire as the two sides spar, with most of the city still largely held by the militants.

“We don’t have enough soldiers,” said Mohammed Qassim, a 25-year-old army soldier. “And the enemy uses every opportunity to advance.”

Mustafa Salim contributed to this report.

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