The Tikrit offensive, launched earlier this week, is the first test of al-Abadi’s ability to orchestrate the recovery of a major city from the Islamic State. It is also an illustration of the government’s deepening partnership with Shiite militia organizations and the military of Shiite neighbor Iran, which has provided advisors, weaponry, training, surveillance and intelligence to counter the militant group.

U.S. officials say two-thirds of the force poised to make an attempt for Tikrit are militiamen rather than Iraqi government forces.

The renewed prominence of Iranian-backed militias — many of them groups U.S. soldiers fought prior to the 2011 U.S. withdrawal — and the increasing openness with which Iranians such as Qassem Soleimani, head of Iran’s elite Qods force, now operate in Iraq has raised alarms in Western capitals and among Iraqi Sunnis.

Militias are already being blamed for abuses in Sunni areas they have cleared of Islamic State militants. But their fighting power is a necessity given the weakened state of Iraqi security forces and the decision by Western countries to keep troops out of combat in Iraq.

The overt Iranian involvement is also a strain on the rekindled U.S.-Iraq military partnership. U.S. soldiers returned to Iraq last summer after Islamic State militants, fueled by the conflict in neighboring Syria, seized much of the north and west of the country.

While the United States and its allies have conducted air strikes across Iraq, U.S. war planes are notably absent in the unfolding battle in Tikrit. In contrast to the hands-off role there, U.S. forces have been playing a major role in helping the Iraqi military prepare for another future urban battle, in Mosul.

Dempsey, who once commanded the U.S. effort to train Iraqi soldiers, has voiced a results-based view of Iran’s military role in Iraq. Earlier this week, he said that Iranian support could be “positive” if it does not spark sectarian tensions.

Now, as he prepares to meet with Iraqi leaders, Dempsey said he was “trying to get a sense for how our activities and (Iran’s) activities are complementary, because we don’t actually coordinate with them directly nor do we intend to.”

Dempsey said the Tikrit campaign — characterized in its early stage by a crowded push of pickup trucks and military vehicles — did not currently qualify as a “sophisticated military maneuver.” He said U.S. and allied air strikes around the refinery city of Baiji had made the Tikrit offensive possible by depriving nearby Tirkit of militant resources.

The Obama administration has been scrambling to reassure allies, especially Arab nations which are partnering with the United States against the Islamic State, about Iran’s military rise in Iraq. During the same trip, Dempsey will also meet with officials in Bahrain, a tiny Gulf nation that is a key U.S. military ally but struggles with Shiite-Sunni tensions of its own.

While Dempsey said Iranian support had made the militias more “tactically effective,” he appeared more skeptical that Iran would play a constructive role once the Tikrit battle ends.

Dempsey said he would ask Iraqi leaders whether Iran shared a U.S. desire to see a multi-sectarian future for Iraq, which U.S. officials say is required to ease the tensions that helped give rise to the Islamic State. “Otherwise,” he said, “it’s just deferring another fight to another day.”

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