<p>A homogeneous moment magnitude (M_W) catalog is essential for robust seismological analysis and seismic hazard assessment, as M_W provides a physically based measure of earthquake size, in contrast to amplitude-based magnitude scales. In Iran, operational earthquake catalogs predominantly report Nuttli (M_N) and local (M_L) magnitudes, whereas the principal large-scale M_W source, the GCMT catalog, has a magnitude of completeness of 5.3 since 1976. This results in a substantial gap in M_W coverage for small-to-moderate earthquakes. Addressing this gap requires region-specific empirical magnitude-conversion relationships; however, most existing models are reliable only for magnitudes larger than about 3.5. In this study, we develop and validate new regional scaling relationships to convert M_N and M_L to M_W for earthquakes with 1.4 ≤ M_L ≤ 5.0 in northeastern and eastern Iran. For the M_L–M_W conversion, we propose both a piecewise linear model with a breakpoint at M_L = 2.9 and a quadratic model. For M_L ≥ 2.9, the two formulations yield closely consistent estimates, differing by no more than ~ 0.1 magnitude units. At lower magnitudes, systematic divergence emerges; for example, an earthquake with M_L = 1.4 corresponds to M_W ≈ 1.9, indicating a difference of approximately 0.5 units. Our proposed linear M_N–M_W relation, valid over the M_N range of 2.0–4.8, exhibits close agreement with the line M_N = M_W. These empirically robust relationships enable the construction of a consistent M_W catalog by correcting magnitude-dependent biases, thereby providing a reliable foundation for improved seismotectonic interpretation and seismic hazard assessment within the study region. Outside this region, these relationships should be applied only provisionally and with caution until local calibrations are developed.</p>