WASHINGTON — Iraqi security forces, backed by American-led air power and hundreds of advisers, are planning to mount a major spring offensive against Islamic State fighters who have poured into the country from Syria, a campaign that is likely to face an array of logistical and political challenges.

The goal is to break the Islamic State’s occupation in northern and western Iraq, and establish the Iraqi government’s control over Mosul and other population centers, as well as the country’s major roads and its border with Syria by the end of 2015, according to American officials.

Iraqi and Kurdish forces have made inroads in recent weeks in securing territory threatened or captured by the Islamic State, including the Rabia border crossing with Syria, the oil refinery in Baiji north of Baghdad, the northern town of Zumar, and Jurf al-Sakhar southwest of Baghdad.

But the major push, which is being devised with the help of American military planners, will require training three new Iraqi Army divisions — more than 20,000 troops — over the coming months.