The coronavirus pandemic (COVID-19) is a global health crisis with a particular emotional and physical impact on health professionals, especially nurses. The aim of this study was to investigate the prevalence of anxiety, depression and fatigue and their possible relationships among nurses during the pandemic. The study population consisted of nurses from five tertiary-level public hospitals in Athens who completed the Fatigue Assessment Scale (FAS), Beck Depression Inventory (BDI) and State-Trait Anxiety Inventory (STAI) questionnaires. Gender, age and years of work experience were recorded. The study was conducted from mid-November to mid-December 2021. The sample included 404 nurses (69 males and 335 females) with a mean age of 42.88 years (SD = 10.90) and 17.96 (SD = 12.00) years of work experience. Symptoms of fatigue were noted in 60.4% of participants, while 39.7% had symptoms of depression, 60.1% had abnormal scores on state anxiety and 46.8% on trait anxiety, with females showing higher scores on all scales (p < 0.05). High positive correlations (p < 0.01) were found between the FAS, BDI, State Anxiety and Trait Anxiety scales. Regression analysis showed that 51.7% of the variance in FAS scores can be explained by trait anxiety, an additional 6.2% by the BDI and 1.2% by state anxiety. Mediation analysis showed that state anxiety and BDI mediate the relationship between trait anxiety and FAS. Finally, BDI was found to exert a moderating role in the relationship between trait anxiety and fatigue. In conclusion, our study showed that nurses continue to experience high rates of anxiety, depression and fatigue. The variation in fatigue appears to be significantly dependent on trait anxiety. Depressive symptomatology and state anxiety exert a parallel positive mediation on the relationship between trait anxiety and fatigue, with depression exhibiting a moderating role in this relationship.