The aim is to add pressure on Islamic State fighters who are being pressed militarily in northeast Syria and Iraq. They are currently partly encircled in Ramadi, the capital of Anbar Province in Iraq, and were recently evicted from Baiji in northern Iraq, site of a strategic oil refinery.

The pesh merga also plan to cut the supply line, Highway 47, the major east-west road that runs past Sinjar and connects Syria to Mosul, Iraq’s second largest city, which the Islamic State captured last year. That would hamper the easy movement of fighters, fuel and supplies within the Islamic State’s self-declared caliphate and force the militants to resort to less efficient smuggling routes.

Still, the operation faces several important military and political challenges.

Even if the Sinjar campaign succeeds, the Islamic State still has a stranglehold on vital areas in the region, including Mosul and large portions of eastern Syria and western Iraq. That includes most of the Sunni Arab heartland of Anbar Province, where a government-led military push has advanced toward Ramadi but has not yet managed to retake it from the Islamic State.

Before the Islamic State swept across northern Iraq, the area was a political stronghold for the Kurdistan Democratic Party of President Massoud Barzani, the leader of the Kurdish autonomous region in Iraq, who is overseeing the Sinjar operation from a command post in northwest Iraq.

But many Yazidis — a tiny religious minority that was almost entirely based around Mount Sinjar before the Islamic State’s advance — blame the pesh merga and the Kurdistan Democratic Party, commonly known as the K.D.P., for failing to prevent Sinjar’s fall in the first place and subjecting them to a catalog of horrors by the Islamic State, including the sexual enslavement of thousands of women.

That calamity led to the flight of hundreds of thousands of Yazidis, tens of thousands of whom spent a week or more exposed to a blazing August sun on the barren slopes of Mount Sinjar with little food or water.