Limited population-based studies discuss the association between fat mass index (FMI) and the risk of liver diseases. This investigation utilized data from the National Health and Nutrition Examination Survey (NHANES) to examine the linkage between the FMI and liver conditions, specifically steatosis and fibrosis. The study leveraged data from NHANES's 2017-2018 cross-sectional study, employing an oversampling technique to deal with sample imbalance. Hepatic steatosis and fibrosis were identified by vibration-controlled transient elastography. Receiver operating curve was used to assess the relationship of anthropometric indicators, e.g., the FMI, body mass index (BMI), weight-adjusted-waist index (WWI), percentage of body fat (BF%), waist-to-hip ratio (WHR), and appendicular skeletal muscle index (ASMI), with hepatic steatosis and fibrosis. In this study, which included 2260 participants, multivariate logistic regression models, stratified analyses, restricted cubic spline (RCS), and sharp regression discontinuity analyses were utilized. The results indicated that the WHR and the FMI achieved the highest area under the curve for identifying hepatic steatosis and fibrosis, respectively (0.720 and 0.726). Notably, the FMI presented the highest adjusted odds ratio for both hepatic steatosis (6.40 [4.91-8.38], p = 2.34e-42) and fibrosis (6.06 [5.00, 7.37], p = 5.88e-74). Additionally, potential interaction effects were observed between the FMI and variables such as the family income-to-poverty ratio, smoking status, and hypertension, all of which correlated with the presence of liver fibrosis (p for interaction < 0.05). The RCS models further confirmed a significant positive correlation of the FMI with the controlled attenuation parameter and liver stiffness measurements. Overall, the findings underscore the strong link between the FMI and liver conditions, proposing the FMI as a potential straightforward marker for identifying liver diseases.