Under the provisions of the Insurance and Reinsurance Business and Other Related Issues Law of 2016 and its subsequent amendments, the Superintendent of Insurance, has no authority to act as a judge or to mediate for the out-of-court settlement of private disputes that arise between insurance companies and policyholders, especially in cases where issues arise in respect to the interpretation and the application of specific terms included in insurance contracts which have been freely signed by the contracting parties involved.  Consequently, he cannot impose the obligation to pay compensation, nor determine its amount, nor interpret the terms of an insurance contract, etc. This authority belongs to the Cypriot Justice.

Despite the above, in an effort to promote the policyholder/consumer protection, the Superintendent of Insurance has issued to the insurance companies specific Orders for complaints handling received by complainants [1]. According to these Orders, the policyholders should first submit in writing their complaints to the insurance companies, which have to officially reply within a maximum period of 45 days. If the insurance company does not answer in time (within 45 days from the date of submission of the complaint) or if the answer provided was vague or unsubstantiated, consumers may submit a relevant complaint to the Superintendent of Insurance. The said complaints are being evaluated by the Superintendent in relation to his supervising authorities.  

Every insurance company has appointed, on the basis of the above mentioned Orders, a person responsible for the administration of complaints received by the company. For contact details for filing complaints with insurance companies click here

Taking into consideration the above, and if you consider the reply of the insurance company to be unsatisfactory, you may submit your complaint to the Cyprus Financial Ombudsman (at the following link, or by telephone at 22848900) who is responsible, under certain circumstances, to examine complaints which fall within his discretion in order to mediate and settle disputes between the two parties.  

Finally, you can take legal action for for resolving your differences in the Courts of Justice of the Republic of Cyprus. 
[1] According to the Order for Complaints Handling a complainant is: a person who is presumed to be eligible to have a complaint considered by an insurance undertaking and has already lodged a complaint, e.g. a policyholder, insured person, beneficiary and injured third party.