To address the challenges and time-consuming manual design of Air Traffic Control (ATC) training scenarios, this paper proposes $\texttt{AirTrafficGen}$, a novel end-to-end scenario generation system leveraging Large-Scale Language Models (LLMs). $\texttt{AirTrafficGen}$ uses graph-based representations to encode sector topology, including airspace geometry, airways, and fixed points, into a format that LLMs can process. Using state-of-the-art models such as Gemini 2.5 Pro, OpenAI o3, GPT-oss-120b, and GPT-5, it generates high-traffic scenarios resembling real-world operations, with engineered prompts providing fine-grained control over the presence, type, and location of interactions. Furthermore, it demonstrates the feasibility of iterative improvement, correcting erroneous scenarios based on simple textual feedback. This system offers a scalable alternative to manual scenario design and contributes to the expansion of the quantity and diversity of ATC training and validation simulations. More broadly, it demonstrates the potential of LLMs for complex planning in safety-critical areas.