Medical training is intensive and predisposes students to psychological distress and burnout. Unaddressed burnout in medical training may persist in the internship phase and impact the quality of patient care. While some associations have been established, the link between some individual factors and training characteristics with distress and burnout in medical training remained unclear. In this study, we aim to examine the prevalence of psychological distress and burnout, and its association with gender, training phase, funding status, cumulative grade points average (CGPA), and coping strategies among medical students. The study applied a multicenter cross-sectional study design and convenience sampling on medical students from two medical schools from Malaysia and India. We used a self-reporting instrument that includes demographic details, the 12-item General Health Questionnaire (GHQ), the Copenhagen Burnout Inventory (CBI), and the Brief Coping Orientation to Problems Experienced (Brief COPE). A total of 748 medical students participated in the study. The prevalence of psychological distress, personal-related, work-related, and patient-related burnout were 33.0%, 56.1%, 35.0%, and 26.2%, respectively. Being male, clinical year, self-funded, and having a CGPA of more than 3.50 predicted psychological distress and burnout with mixed results. Maladaptive coping mechanisms consistently predicted the risk of psychological distress and burnout by more than two times. The findings indicate that primary and secondary mental health interventions have a role in medical training. A systematic intervention should incorporate coping skills training alongside institutional-targeted intervention.