Saudi Arabia's cabinet is officially referred to as the Council of Ministers, which is a direct translation from Arabic.

Rather than "premier" or "prime minister," the title of "Chairman of the Council of Minister" is officially preferred.

"Office" would be my preference, but "Diwan" is also commonly used.

The King is the holder of this office.

Please take a look at this page:

http://www.servat.unibe.ch/icl/sa06000_.html

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Note added at 4 hrs (2008-08-30 18:52:51 GMT)
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One more point:

In Saudi Arabia, the King (Ch. of the C. of M.) is not referred to as "His Royal Highness." That title is reserved for princes (and princesses) other than the King.

Kings and Queens usually take the title of "His/Her Majesty," and that used to be the case in Saudi Arabia as well, until the late King Fahd, egged on by some overzealous verbal engineers, one day decided he no longer wanted "Majesty" associated with his name. Instead, he opted for

خادم الحرمين الشريفين

"Servant of the Two Honorable Mosques."

For some unknown reason, the title was officially translated to "Custodian of the Two Holy Mosques." King Abdullah, Fahd's successor, has kept this tradition.

There is no need to insert this honorific title in your text.

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Note added at 7 days (2008-09-06 18:20:49 GMT)
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The difference between the King's duty as Chairman of the Council of Ministers and as Prime Minister is that the latter does not exist in Saudi Arabia. It could conceivably exist if the King were to relinquish his executive office and give it to someone else. That other person would then become a minister to the King, a "PRIME" minister to whom other ministers report. But with the king himself heading the cabinet, he could not be called a "minister," even a "prime" one.

This is even clearer in Arabic, where the word WAZEER essentially means "assistant."

Notice that in Arabic, the King of Saudi Arabia is never referred to as رئيس الوزراء

He is always رئيس مجلس الوزراء

In other words, he is the head of the cabinet as an institution. He is not a chief minister, because he does not report to anyone. It would be nice if he could think of himself as minister to the people, but so far, that has not been part of the equation.

A similar situation exists in the U.S., where the system is presidential, i.e., the president is not only the head of state, but also the head of the government -- the chief executive officer. If the head of the cabinet were someone other than the president, that person could be called a "chief secretary" or some other conceivable appellation. But so long as the system remains presidential, the president is just the president. His executive function is referred to simply as "chief executive" or "head of the cabinet" (no capital letters, since these are not titles, just functional descriptions).

That is part of the rationale of this unusual appellation in Saudi Arabia, but it may be an after-the-fact rationale. The title may simply have been a direct translation from the Arabic, and it stuck, for better or worse.