Suicide is a major public health concern and a multidimensional phenomenon whose incidence has been steadily increasing among young populations worldwide. Psychosocial, cognitive, and biological factors play a central role in suicidal behavior. A deeper understanding of these risk and protective factors is essential to generate early alerts and guide the design of preventive interventions. This study aimed to analyze the effect of selected psychosocial and family-related variables on suicide risk in university students, as part of the project Risk factors and psychosocial predictors related to suicidal behavior in university students: a multicenter comparative study. A total of 2392 subjects from four countries (Colombia, Spain, Mexico, and Bolivia) participated in the study. Data were analyzed using multinomial logistic regression to evaluate three psychosocial variables—family history of mental illness, family history of suicide, and self-perceived health status—and one family-related psychological variable: family functioning. Suicide risk was categorized into low, medium, and high levels. Odds ratios (OR) and 95% confidence intervals (CI) were calculated. Family history of suicide emerged as the strongest predictor, increasing the probability of belonging to the high-risk group more than threefold and to the medium-risk group more than tenfold, compared to the low-risk group. In contrast, both positive self-perception of health and higher family functioning were significantly associated with lower probabilities of medium and high suicide risk, highlighting their protective effect. Family history of mental illness did not show a statistically significant association with suicide risk in this model. The findings emphasize the need for preventive strategies that include psychosocial support for relatives of suicide victims and interventions focused on strengthening family dynamics. Promoting positive health perceptions and enhancing family functioning may help reduce suicide risk in young populations. These results contribute valuable evidence for the design of targeted public health and university-based suicide prevention programs.