Army Gen. Martin Dempsey earlier this month. (Joshua Roberts/Reuters)

The top U.S. military officer will press the government of Iraqi Prime Minister Haider al-Abadi during a visit to Iraq this week about its plans for avoiding sectarian fallout once the Iranian-backed operation to dislodge the Islamic State from the city of Tikrit concludes.

Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, said he was confident that Iraq would ultimately defeat the Sunni militants in Tikrit, a largely Sunni city northwest of Baghdad. He said the group’s fighters number only in the hundreds there, while the force of Iraqi troops and Iranian-backed militia fighters advancing on the city stands around 23,000.

“The important thing about this operation in Tikrit in my view is less about how the ­military aspect of it goes and more about what follows,” he told reporters ahead of a visit to Iraq, where he will meet with the Shiite-led government. “Because if the Sunni population is then allowed to continue to live its life the way it wants to, and can come back to their homes . . . then I think we’re in a really good place.

“But if what follows the Tikrit operation is not that, if there’s no reconstruction that follows it, if there’s no inclusivity that follows it, if there’s the movement of populations out of their homeland that follows it, then I think we’ve got a challenge in the campaign.”

The Tikrit offensive, launched this past week, is the first test of 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 advisers, weaponry, training, surveillance and intelligence to counter the militant group.

Iraqi forces and Shiite militiamen inch closer to Tikrit as fighting with Islamic State continues. (Reuters)

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 Iran-backed militias — many of them groups U.S. troops fought prior to the 2011 U.S. withdrawal — and the increasing openness with which Iranians such as Maj. Gen. Qasem Soleimani, head of Iran’s elite Quds Force, now operate in Iraq has raised alarms in Western capitals and among Iraqi Sunnis.

Militias are 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 there.

The overt Iranian involvement also puts 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.

Although the United States and its allies have conducted airstrikes across Iraq, U.S. warplanes 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. This past week, he said that Iranian support could be “positive” if it does not spark sectarian tensions.

As he prepared 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.”

Iraqi forces launch an assault to retake an area northeast of Al-Garma district in the Sunni heartland of Anbar province from Islamic State. (Reuters)

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

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

Although 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 shares 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.”