Traffic signal control is a critical task in intelligent transportation systems, yet conventional fixed-time and rule-based methods often struggle to adapt to dynamic traffic demand and provide limited decision interpretability. This study proposes an LLM-augmented traffic signal control framework that integrates LSTM-based short-term traffic state prediction, predictive phase selection, structured large language model reasoning, and safety-constrained action filtering. The LSTM module forecasts future queue length, waiting time, vehicle count, and lane occupancy based on recent intersection-level observations. A predictive controller then generates candidate signal actions, while the LLM module evaluates these actions using structured traffic-state inputs and produces congestion diagnoses, phase adjustment recommendations, and natural-language explanations. To ensure operational reliability, all LLM-generated recommendations are validated by a safety filter before execution. Simulation-based experiments in SUMO compare the proposed method with fixed-time control, rule-based control, and an LSTM-based predictive baseline under balanced demand, directional peak demand, and sudden surge scenarios. The results indicate that the proposed framework improves traffic efficiency, especially under dynamic and non-recurrent traffic conditions, while maintaining zero constraint violations after safety filtering. Overall, this study demonstrates that LLMs can enhance traffic signal control when used as constrained reasoning and decision-support modules rather than direct low-level controllers. Keywords: Intelligent Transportation Systems; Traffic Signal Control; Large Language Models; LSTM; Traffic State Prediction; Decision Support; Safety-Constrained Control; SUMO Simulation.