Urban traffic management faces significant challenges due to the dynamic environments, and traditional algorithms fail to quickly adapt to this environment in real-time and predict possible conflicts. This study explores the ability of a Large Language Model (LLM), specifically, GPT-4o-mini to improve traffic management at urban intersections. We recruited GPT-4o-mini to analyze, predict position, detect and resolve the conflicts at an intersection in real-time for various basic scenarios. The key findings of this study to investigate whether LLMs can logically reason and understand the scenarios to enhance the traffic efficiency and safety by providing real-time analysis. The study highlights the potential of LLMs in urban traffic management creating more intelligent and more adaptive systems. Results showed the GPT-4o-mini was effectively able to detect and resolve conflicts in heavy traffic, congestion, and mixed-speed conditions. The complex scenario of multiple intersections with obstacles and pedestrians saw successful conflict management as well. Results show that the integration of LLMs promises to improve the effectiveness of traffic control for safer and more efficient urban intersection management.