Suicide is a leading cause of death, and the last decades of research have identified a range of risk factors for it, including age, sex, a history of self-injury and suicide attempts, and explicit suicide cognitions. More recently proposed risk factors also include implicit self-harm and suicide cognitions. However, most studies have only examined these risk factors in isolation, and little is known about their combined effect and potential (non-linear) interactions in the prediction of self-harm and suicide. We analyzed an online community sample of 6,855 participants whose implicit self-harm and suicide cognitions were measured using the Implicit Association Task (IAT). We used different machine learning techniques to evaluate the utility of these implicit cognitions to predict concurrent desire to self-harm or die. Desire to self-harm was best predicted using gradient boosting, achieving 83% accuracy, while desire to die was best predicted using regularized logistic regression, achieving 80% accuracy, both using explicit and implicit predictors. However, the most important predictors were mood, explicit associations between the self and self-harm or suicide, and past suicidal thoughts and behaviors; implicit measures led to little to no gain in predictive accuracy. Our findings challenge the use of implicit suicide cognition measures in the prediction of concurrent suicidal ideation. We outline the implications of our findings with respect to the use of suicide/death IATs in clinical settings, and we describe directions to further assess the predictive utility of IATs in the prospective prediction of suicidal thoughts and behaviors.