The objective of this study was to assess the effects of different warning messages for an Intersection Movement Assist (IMA) based on drivers' ability to avoid a potential safety hazard. An IMA system can detect hazards and warn drivers when it is unsafe to enter an intersection. The effects of different warning information conveyed by these systems are still unknown. A driving simulator study with 80 participants was conducted with a red light running (RLR) scenario using a 5 (warnings) x 2 (training) between-subject design. IMA warnings included the messages "Danger," "Brake now," "Vehicle on your left," a beep, and no IMA warning. Training was provided to half of the participants. Analysis of variance and logistic regression models were used to examine differences in drivers' avoidance behavior. The analyses showed that all tested warning messages can significantly enhance drivers' avoidance performance. Significant differences were observed in crash occurrence, avoidance behavior (i.e., reaction time and speed change), and eye movements (i.e., fixation pattern and time to first fixation). The effects of training also differed given the warning message provided. The "Brake now" message performed best in reducing crash involvement and prompted better avoidance performance. The "Danger" and "Vehicle on your left" messages improved drivers' hazard detection ability. The training showed a potential to enhance the effectiveness of nonspeech warning messages. The findings of this study can help designers and engineers better design IMA warning messages for RLR scenarios.