The steady growth of Shiite militias in Iraq is making it increasingly difficult for American forces deployed there to determine exactly which Iraqi forces they are supporting, experts say.

The official line from Defense Department is that the U.S. will support operations involving both the Iraqi army and some militia forces that are operating "under command and control of the Iraqi government."

But the Pentagon wants to avoid providing direct support for anti-Islamic State militia forces loyal to Iran, a longtime enemy, a reflection of the deeply opaque and tumultuous politics of the Middle East.

"I love this line, 'We only want to support the militias under the command and control of the Iraqi government.' You can't really look at it that way. There is a lot of fuzzy gray area in that zone," said Phillip Smyth, an adjunct fellow at the Washington Institute for Near East Policy.

"It's not some binary situation like people keep trying to make it out to be," Smyth said.

The chain of command in Iraq has frayed since the Islamic State's battlefield victories last year inspired the creation of the so-called Popular Mobilization Forces, or PMF, a loose-knit patchwork of mostly Shiite militias with scattered loyalties to leaders in both Iraq and Iran.

The PMF are not part of Iraq's Ministry of Defense, which has close ties to the U.S. military after years of receiving money and training from Americans. Instead, the PMF militias operate — technically — under Iraq's Ministry of Interior, which has direct links to Iran.

The head of the Ministry of Interior, Mohammed Salem Al-Ghabban, is a Shiite who was imprisoned under former Iraqi dictator Saddam Hussein's regime and later lived and attended a university in Tehran, the capital of Iran. He is a member of the Badr Organization, a Shiite political party with close ties to Tehran.

For many factions of the PMF, it appears that their chain of command leads to both the Iraqi and Iranian government.

"There's a formal line that says, 'We work for the [Ministry of Interior of Iraq], but there is also an informal line with these groups that have pledged loyalty to Tehran and the Ayatollah Khamenei," said Rick Brennan, a senior political scientist at the Rand Corp. who has worked extensively with U.S. forces in Iraq over the past decade.

"It's a shadow military operating side by side, if you will, with the Iraqi government forces. But these are the forces that the U.S. says it will not support. It becomes very difficult when you try to identify where the units that we'll be supporting are," Brennan said.

"What [U.S. Central Command] is trying to do is to focus on providing support to the Ministry of Defense and the brigades that are fighting ISIS," Brennan said, referring to the Islamic State, which is also known as ISIS or ISIL.

It's not clear which force — the U.S.-aligned Iraqi Army or the PMF forces tied to Iran — is larger or more powerful.

The PMF militias are now estimated to number up to 120,000, experts say.

Technically, the Iraqi army is larger, but pervasive corruption makes its precise size difficult to pin down. Last year, Iraqi Prime Minister Haider Al-Abadi acknowledged that the Iraqi army was paying salaries to at least 50,000 "ghost soldiers" who existed only on paper, presumably because officers were skimming money from the cash-based payroll system.

Some of Iraq's forces, particularly special operations teams, have sophisticated training and equipment. But among other segments of the rank-and-file force, motivation, morale and will to fight are in question.

Many of the Shiite militias are essentially the same groups that U.S. forces faced in direct combat a decade ago. An estimated 500 American combat fatalities were linked to Iran and the Shiite militias they supported, according to U.S. defense officials.

U.S. military leaders consider the Iranian-backed militias in Iraq to be potential adversaries.

"When you talk to military people who have fought in Iraq and they are looking at all of these individuals who are now part of the Popular Mobilization Force, they are the worst of the people who were fighting the U.S. when we were there," Brennan said. "They all have blood on their hands, and there is an uneasiness about where this leads."

With more than 100,000 Shiite militia troops roaming around the Iraqi battlefield, U.S. officials are treading cautiously and adjusting their tactics accordingly.

"I think that's one of the main reasons why we are not launching more airstrikes than we are now," said Nathaniel Rabkin, managing editor of Inside Iraqi Politics, a political newsletter.

"U.S. military planners are very afraid of a situation where we end up with some kind of friendly fire incident with Shia militias," Rabkin said in an interview.

"For some of the more radical Shia militias, there is a common belief that the U.S. somehow provides covert support to ISIS — which is a very strange thing and very difficult for a lot of Americans to believe. But there are people who believe that and believe the U.S. is trying to undermine the efforts of these Shia militias," Rabkin said.

"The U.S. wants to avoid a situation where we see guys running around the desert in pickup trucks, assume they are ISIS, bomb them and they are actually Shiite militias — and they say, 'Oh see, look, the Americans are targeting us,' " he said. "That is the kind of grim worst-case scenario we are looking at."

Conspiracy theories about the U.S. secretly supporting ISIS are aggressively pushed by Iranian leaders, who often declare publicly that the U.S. created ISIS and conspires with them in an effort to divide Muslims and erode Iran's regional influence.

That propaganda campaign fuels American concerns that the Shiite militias that share this anti-ISIS agenda could turn their guns on U.S. forces at any time.

"I think DoD as a whole is preparing just in case these Shiite militias decide to press the button and start hitting American interests. I think they see a problem there," Smyth said.

High-level policy decisions from Washington may not be all that responsive to the the day-to-day questions facing U.S. troops in Iraq about who to support with air strikes and when, he said.

"I'm pretty sure you have a lot of people over there sitting in a room shaking their heads in silence."