The article discusses the possibility to resolve a political conflict between the Prime Minister and the President of the Republic regarding the appointment of a member of Government in the proceedings on disputes about the scope of competence of public authorities in the Constitutional Court. In addition, it analyses the possible reasons for the President not to appoint the person nominated by the Prime Minister and from this point of view, it evaluates the concrete reasons given by the President in two cases from 2019 and 2021.