While the complexity of fifth-generation wireless networks is being widely commented upon, there is great anticipation for the arrival of the sixth generation (6G), with its enriched capabilities and features. It can easily be imagined that, without proper design, the enrichment of 6G will further increase system complexity. To address this issue, we propose the Agentic-AI Core (A-Core), an artificial intelligence (AI)-empowered, mission-oriented core network architecture for next-generation mobile telecommunications. In A-Core, network capabilities can be added and updated on the fly and further programmed into missions for enabling and offering diverse services to customers. These missions are created and executed by autonomous network agents according to the customer’s intent, which may be expressed in natural language. The agents resolve intents from customers into workflows of network capabilities by leveraging a large-scale network AI model and follow the workflows to execute the mission. As an open, agile system architecture, A-Core holds promise for accelerating innovation and greatly reducing standard release times. The advantages of A-Core are demonstrated through two use cases.