You do NOT "completely control the Near East region", so you have probably missed a barony somewhere. Or, less likely, you have missed some counties due to misunderstanding the borders of the Near East region.
To check for missing baronies:
--- Go to the councillor job screen
--- Click the button which assigns your Chancellor (diplo councillor) to
"Sow Dissent"
--- Any county which is highlighted in green contains a barony which is NOT part of your realm
--- There must be no green-highlighted counties in the Near East region (see below)
To check the border of the region:
--- Find a county in the region (eg. Jerusalem)
--- Left-click on it, so the holdings window appears in the bottom left of the screen
--- Find the tiny blue and green "regions" button, in the top right of the holdings window
--- Click the "regions" button until it is displaying the borders of the Near East
--- Check that the green outline on the map is always on or inside your border
Extra tip:
--- If some of the baronies you need are owned by holy orders of your religion, it can be very hard to take them. (Because the de jure barony CB is disabled against holy orders of your religion.)
--- The easiest way to take them is: convert to another religion, declare war, win, convert back to your original religion.
--- Since you own Jerusalem, this should be super-easy: right-click on the coat of arms for Jerusalem; secretly convert to Orthodox/Nestorian (Islam is not recommended because it'll change your succession law and add/remove religious traits) (-250 piety); right-click on your portrait; personally adopt faith; declare war; win; right-click on your portrait; convert to capital religion (-1000 prestige +250 piety).