"Iran’s vision is creating an Iraqi Hezbollah. They were hoping that Moqtada al-Sadr could become the Hassan Nasrallah of Iraq, the leader of an Iraqi Hezbollah-type political party that would be both a militia and a political party that could also provide social services. It’s a model that has served them well in Lebanon," said Molavi.

Another Washington analyst, Fred Kagan at the American Enterprise Institute, said Iraq charts its own course, but often works in concert with Iran.

"Fundamentally, Iraq is acting, at this point, in the region as an ally of Iran on a state-to-state level in terms of its support for [Syrian President] Bashar al-Assad, in terms of Dawaa support for oppositionists in Bahrain, and just in terms of allowing the Iranians to flout the [UN, U.S. & E.U.] sanctions regimes in an outrageous fashion."

Molavi said the Iraq-Iran relationship is a matter of cold pragmatism and opportunism. "At the end of the day, I mean, these are amoral national interest states. You know, and these amoral national interest states will find reasons, you know, to shunt aside their ideologies, their religious affiliations, their sectarian identities, if they feel it’s both in the national interest of their state, but also, in the personal interest of their political elites."

Analysts say the emerging Iran-Iraq relationship compels the U.S. to accept that no one state will be able to control the outcomes in the volatile Persian Gulf.