How can the public sector use AI ethically and responsibly for the benefit of people? The sustainable development and deployment of artificial intelligence (AI) in the public sector requires dialogue and deliberation between developers, decision makers, deployers, end users, and the public. This paper contributes to the debate on how to develop persuasive government approaches for steering the development and use of AI. We examine the ethical issues and the role of the public in the debate on developing public sector governance of socially and democratically sustainable and technology-intensive societies. To concretize this discussion, we study the co-development of a Finnish national AI program AuroraAI, which aims to provide citizens with tailored and timely services for different life situations, utilizing AI. With the help of this case study, we investigate the challenges posed by the development and use of AI in the service of public administration. We draw particular attention to the efforts made by the AuroraAI Ethics Board in deliberating the AuroraAI solution options and working toward a sustainable and inclusive AI society.