The promising potential of AI and network convergence in improving networking performance and enabling new service capabilities has recently attracted significant interest. Existing network AI solutions, while powerful, are mainly built based on the close-loop and passive learning framework, resulting in major limitations in autonomous solution finding and dynamic environmental adaptation. Agentic AI has recently been introduced as a promising solution to address the above limitations and pave the way for true generally intelligent and beneficial AI systems. The key idea is to create a networking ecosystem to support a diverse range of autonomous and embodied AI agents in fulfilling their goals. In this paper, we focus on the novel challenges and requirements of agentic AI networking. We propose AgentNet, a novel framework for supporting interaction, collaborative learning, and knowledge transfer among AI agents. We introduce a general architectural framework of AgentNet and then propose a generative foundation model (GFM)-based implementation in which multiple GFM-as-agents have been created as an interactive knowledge-base to bootstrap the development of embodied AI agents according to different task requirements and environmental features. We consider two application scenarios, digital-twin-based industrial automation and metaverse-based infotainment system, to describe how to apply AgentNet for supporting efficient task-driven collaboration and interaction among AI agents.