Pssst, this is in American "controlled" Iraq, NOT Iran.
To be fair though, it appears from the language they aren't demanding they actually convert, but rather that they wear the veil (and whatever "possessing the honorable teachings of Islam" is.
What kind of "honor" is it that threatens people with such crimes?
For more on the "honorable teachings of islam" please see:
http://www.prophetofdoom.net/
I don't understand why we would want to enter into negotiations with a country that butchered hundreds, if not thousands, of innocent civilians and political dissidents in Lebanon, Israel, Argentina, Germany, and countless nations throughout the civilized world.
It just doesn't make sense to me.