I am Belgium and although I married a Moslem Israeli Arab man at the Shaaria court, the Israeli Ministry of Interior refuses to register our marriage. Can we bring legal action to make it do so?

Yes! You can file a joint application for a civil court order against the Ministry of Interior, to issue a specific order obliging it to register your marriage, to either the family court or a special administrative court, depending on the circumstances.

Further details are needed, so that individual and personal legal counselling can be given, It may be worthwhile considering drawing up a family life agreement in the meantime, and getting it authorized at the family court, in order to support and strengthen an application, which you need to file anyway, to regulate and secure your status in Israel, as the partner of an Israeli citizen.