The United States now has about 3,000 troops, including trainers and advisers, in Iraq. But the steps envisioned by the White House are likely to be called half-measures by critics because they do not call for an expansion of the role of American troops, such as the use of spotters to call in airstrikes.

There has long been debate within the administration about what the first steps in the campaign should be.

Led by Gen. Lloyd J. Austin III, the Central Command has long emphasized the need to strike a blow against the Islamic State by recapturing Mosul, Iraq’s second-largest city, which was taken by the group in June 2014. Mosul is the capital of Nineveh Province in northern Iraq and was the site of a sermon that Abu Bakr al-Baghdadi, the leader of the Islamic State, defiantly delivered in July. The Baiji refinery, a major oil complex, is on a main road to Mosul.

While General Austin was looking north, State Department officials have highlighted the strategic importance of Anbar Province in western Iraq.