LALISH, Iraq—Pir Said stood reverently barefoot, like all those in the inner temple sanctuary, on the warm inner stone courtyard of the holiest shrine in the Yazidi faith, the tomb of Sheikh Adi in the town of Lalish.

Lalish, in Iraq's northern Kurdish mountains, is to the Yazidis what Mecca is to Muslims, or what Jerusalem is to followers of the three great monotheistic faiths: Islam, Christianity, and Judaism.

It is the holiest site of an ancient Kurdish minority faith whose members have been in flight since early August, scattered by the tempestuous advance of Islamic State (IS) insurgents into Sinjar, a majority Yazidi town in northwestern Iraq, and its surroundings.

The Yazidis were propelled into the international spotlight last month, when