Income inequality is one of the fundamental challenges of the Iranian economy, especially under sanctions and macroeconomic fluctuations. The present study aims to investigate the impact of government public debt and foreign direct investment (FDI) on income inequality in Iran during the period 1991–2023. For this purpose, a mixed approach including the autoregressive distribution lag (ARDL) model, threshold regression with network search method, random forest model, shock response functions (IRF) and three-dimensional interaction analysis has been used. The findings show that the relationship between public debt and income inequality is nonlinear and U-shaped; Thus, at low levels of debt (less than the threshold of 1,275,848,288 billion rials), increasing debt has a negligible or decreasing effect on inequality, but crossing this threshold is associated with a significant increase in inequality. Also, foreign direct investment has a significant decreasing effect on the Gini coefficient with a two-year lag, although this effect is temporary in the short term. The results of the Random Forest model show that government final consumption, with a relative importance of 0.316, is the most important determinant of inequality in Iran, and the role of FDI and public debt appears much less and mainly through interactions