Iraqi forces are on a westward push to retake Anbar, a sprawling Sunni-dominated desert province captured by the Islamic State group in their offensive last year. But as the battles for Tikrit and Ramadi have shown, it will be a hard slog for a much-diminished Iraqi army — especially given Baghdad's reticence to arm Sunni tribesmen and local fears of the Shiite militias backing government forces.

Earlier this month, Iraqi forces captured the northern Sunni-majority city of Tikrit from the Islamic State group, but only with the backing from Iranian-trained and Iran-funded Shiite militias and U.S. airstrikes — methods that cannot work in Anbar province.

The past weeks of seesaw battles in Anbar, with progress in areas like Garma east of Fallujah, a stalemate in the biggest city of Ramadi and an Iraqi rout near Lake Tharthar, show that the army still needs help. But relying on erstwhile Shiite militia allies may not be palatable to locals.

"The Iraqi soldiers fighting in Anbar are not well-trained enough for this battle. Many of the soldiers are there for the money, but the (Shiite militias), they are believers in this fight," said an Iraqi brigadier general involved in the Anbar campaign. "There isn't yet a clear plan to liberate Anbar because of the political and tribal disputes."

Speaking on condition of anonymity because he was not authorized to speak to journalists, he said some tribes might be supportive but others were with the Islamic State group. He also lamented how soldiers would throw down their weapons and flee when hard-pressed.

On Friday, government reports of advances in Anbar were belied by an Islamic State attack on a water control system on a canal north of Islamic State-occupied Fallujah that killed a division commander and at least a dozen soldiers.

In the past few years, Iraq's army has been hollowed out by corrupt commanders siphoning off salaries and equipment and not training soldiers to do much more than man checkpoints.

A force that once numbered in the hundreds of thousands is now estimated by U.S. officials to be around 125,000 at best and probably a lot less, once all the so-called "ghost-soldiers" — non-existent names on the payroll — are purged.

The army has had some victories around Baghdad and in the eastern Diyala province with the help of Shiite militias. But if they were used in Anbar, it would only further alienate the Sunni population in the province, where the Islamic State group has been entrenched since January 2014.

Dhari al-Rishawi, a Sunni tribal leader in Anbar who helped form the Sunni militias known as Sahwa or Awakening Councils, which with the U.S. military drove al-Qaida out of the province in 2006, said people are terrified that the army will be bringing the Shiite militias.

"We know that if the militias are involved, there will be Iranian advisers and that would be a disaster because in this region there is a lot of sensitivity over Iranian interference," al-Rishawi told The Associated Press. "The tribes of Anbar are ready to fight the Islamic State and eject them but on the condition that the state arms them."

Plans to create a National Guard with Sunni fighters have stalled because the Shiite-dominated government suspects many of supporting the Islamic State group and refuses to arm them.

Under the former Prime Minister Nouri al-Maliki, the Sunni Awakening force was dismantled after the U.S. pulled out in 2011, further alienating the local population.

Since taking over large parts of the province, the Islamic State group hasn't been idle.

"In one and a half years, ISIS has become embedded within the civil structure of many portions of Anbar province and they have killed a lot of people that oppose them and the government wasn't able to do anything," said Richard Brennan, an Iraq expert at the Rand Corporation, using an alternate acronym for the group. "The government has to convince those remaining that it's worth the risk to oppose ISIS."

With the Islamic State in control of large parts of Ramadi as well as all of Fallujah — a city the U.S. military only retook with difficulty in 2004 — the Iraqi troops have some incredibly difficult urban fighting ahead of them. Also, the U.S.-led coalition would be unable to back the Iraqis with air power in dense urban combat.

So far, the bulk of the fighting has been done by the Iraqi special forces division, which continued to be trained and equipped by the Americans even after the U.S. withdrawal, but they can't be everywhere and the regular Iraqi army often hasn't been able to hold on to its gains.

In some places, it is the militias that have played this role, but that wouldn't agree with the disaffected Sunnis of Anbar.

"We are caught between the hammer of the Islamic State and the anvil of the militias and we don't know where to go," al-Rishawi said.