Translation:The prime minister and his ministers.
In American English, minister means a religious person usually from a Protestant faith. The actual word for a member of the cabinet of the President of USA is Secretary. The same applies when talking of Secretaries of Parliamentary systems like in the UK. I believe that "ministers" are used in other European and Latin American countries to indicate the same as Secretaries in the USA. If I translate Minister as Secretary, it should be accepted. The only exception is Prime Minister.
'Secretary of State', by all means. But US presidents also have secretaries of the commoner kind to draft letters and type out memos (and, in the case of some of them, other things entirely).
If you don't add 'of State', I really don't think the sentence 'the prime minister (or president, if you like) and his secretaries' would normally be interpreted in the way you describe at all.
Definitely, Secretary conveys the title of each member of the cabinet of the President of the USA as well as the MPs who are members of the cabinet of the Prime Minister of the UK with the exception of the Chancellor of the Exchequer who is equivalent to the Secretary of Treasury of the USA. Now, because of the use of Minister as members of the Cabinet of Presidents in European democracies, I am sure people in the USA will understand the meaning if you use "minister" instead of Secretary.