Officials and military analysts agree that a sprawling battle to drive the Islamic State out of Anbar and its stronghold in Mosul will take a much bigger force than is gathered around Tikrit.

The progress in Tikrit raises the possibility of increased cooperation among the militias, the army and Kurdish pesh merga forces, including those battling ISIS nearby around the northeastern oil hub of Kirkuk. But it will not be as simple as just having those two sets of forces link up and march onward.

In particular, there are mounting concerns about sectarian tension. Most of the forces around Tikrit are made up of Shiite militiamen, who are being guided by Iranian military advisers. Their advance into heavily Sunni areas has worried some American officials, and the United States-led coalition has not yet conducted airstrikes centered directly on the Tikrit mission.

Given those concerns, as well as political and ethnic tensions and differing terrain and battle dynamics, a lineup of forces that works on one front may not work on another, analysts and officials say. Yet it is hard to see how a large enough force to take Mosul — with hundreds of thousands of residents and thousands of ISIS fighters — could be built without drawing on all the available forces, regardless of the difficulties.

Iraqi officials insist that their urgent efforts to build up the regular army, with the help of American trainers, will deliver at least two or three more divisions — thousands of troops, theoretically — to help with the Mosul offensive. But recruiting and retraining efforts for the Iraqi Army have not produced as many fighters as the parallel efforts by Shiite militias.

At times, Shiite forces and pesh merga have cooperated against the Islamic State, and Iraqi officials say both groups operate under the central military chain of command. But they have been at best only loosely subsumed. And neither is well suited to Anbar, a province dominated by Sunni Arab tribes and a longtime cradle of Iraqi insurgencies. ISIS leaders first came together battling the United States occupation there.