Artificial intelligence is moving from experimental laboratories into the ordinary work of public administration. Governments increasingly use algorithmic systems to allocate benefits, detect fraud, assess risk, prioritize inspections, and support decisions affecting migration, policing, employment, and access to public services. These systems may improve consistency and administrative capacity, but they also create constitutional and democratic risks when their logic is opaque, their data reproduce historical inequalities, or their outputs are treated as neutral facts rather than contestable judgments. This article examines the relationship between algorithmic governance and the rule of law through a doctrinal and comparative analysis of European legal instruments and international principles. It argues that legality cannot be protected by transparency alone. Public-sector artificial intelligence requires a layered accountability model combining a clear legal basis, impact assessment before deployment, meaningful human responsibility, procedural rights for affected persons, independent oversight, and continuous auditing after implementation. The article compares the European Union Artificial Intelligence Act, the General Data Protection Regulation, the Council of Europe Framework Convention on Artificial Intelligence, and the UNESCO Recommendation on the Ethics of Artificial Intelligence. It concludes that the central policy question is not whether governments should use algorithmic systems, but under what institutional conditions automated assistance can remain subordinate to public reason, equality, and reviewable human judgment.