Background and Objective The COVID-19 pandemic has been linked to an increase in psychological distress and mental disorders worldwide. The objectives of this study were to investigate the correlates of psychological distress during the COVID-19 pandemic and explore whether the relationship between stress and psychological distress was mediated by cognitive emotion regulation strategies and sleep.Methods Four hundred ninety-six university students completed the Mental Health Inventory, the Insomnia Scale, the Cognitive Emotion Regulation Questionnaire, and the Perceived Stress Scale.Results Female gender and younger age were related to stress, sleep difficulties, and psychological distress. Stress was positively correlated with psychological distress and these two variables were associated with sleep difficulties, negative cognitive emotion regulation strategies (both positively), and positive cognitive emotion regulation strategies (inversely). In mediation analyses, there was a statistically significant positive direct/indirect impact of stress on psychological distress. The indirect pathways linking stress to psychological distress were: through an increase in negative cognitive emotion regulation strategies or a reduction in positive ones; through sleep difficulties; and through negative cognitive emotion regulation strategies and sleep. Female gender had a positive impact on sleep difficulty index, negative cognitive emotion regulation, and psychological distress.Conclusions The cognitive-emotional arousal associated with stress, as well as the maladaptive cognitive emotion regulation to cope with stress, may be implicated in the genesis and maintenance of sleep difficulties and distress during the pandemic. Strategies that include stress management, emotional self-regulation, and sleep hygiene should be implemented to promote the mental/psychological well-being of university students in future public health crises, such as the COVID-19 pandemic.