Intersection safety evaluation has primarily relied on historical crash data. However, due to several limitations, including rarity, unpredictability, and irregularity of crash occurrences, quantitative and qualitative analyses of crashes may not be accurate. To transcend these limitations, intersection safety can be proactively evaluated by quantifying near-crashes using alternative measures known as surrogate safety measures (SSMs). This study focuses on developing models to predict critical near-crashes at signalized intersections based on SSMs and kinematic data. This study used extracted road-users trajectories from video data from ten signalized intersections in the city of San Diego and the Next Generation Simulation (NGSIM) datasets to investigate the near-crash prediction models for bicycle-vehicle and vehicle-vehicle conflicts. Machine learning methods including logistic regression (LR), support vector machine (SVM), random forest (RF), and neural network (NN) were employed to develop prediction models. A variation of time to collision called T2 and Post encroachment time (PET) was used to specify monitoring periods and identify critical near crashes. Four scenarios were created using two thresholds of 5 and 3 s for both PET and T2. In each scenario, various monitoring period lengths were examined. The RF model was superior to other models in almost all different scenarios and across different monitoring period lengths. Vehicle-vehicle scenarios performed slightly better than bicycle-vehicle models, with recall rates above 85%. Sequential backward and forward feature selection methods were applied to bicycle-vehicle near-crash prediction models, which enhanced model performance, resulting in 85% or higher recall values across all scenarios. Considering only rear-end conflicts for both vehicle-vehicle and bicycle-vehicle interactions, critical near- crash prediction models showed performance improvements across all evaluation metrics.