The early bombardment history of Mars may have drastically shaped its crustal evolution. Impact-induced melting of crustal and mantle materials leads to the formation of local and regional melt ponds, and the cumulative effects of the impact flux could result in widespread melting of the crust. To quantify impact-melt production, its provenance and final distribution as a function of impact conditions, we carried out a systematic parameter study using the iSALE shock physics code. In contrast to simplified scaling laws for estimating the amount of melt generated by shock compression, we take the planet's thermal state at the time of impact into account. In addition, we consider decompression melting as a consequence of lithostatic uplift of initially deep-seated material. We find that the geothermal profile has a strong effect on melt production, and that melt volumes are significantly increased by up to a factor of seven in comparison to existing analytical estimates. Enhanced melting occurs at impactor sizes (and velocities) that deposit most of their energy at a depth close to the base of the lithosphere. Impactors larger than 10 km penetrate through the lithosphere and can generate a significant amount of melt by decompression due to lithostatic uplift, which can make up to 40% of the total melt volume. In some cases, the total melt volume exceeds the volume of the transient (and final) crater and the surface expression of these collisions may resemble large igneous provinces rather than typical craters. •Melt production on early hot Mars is increased by up to 7× compared to scaling laws.•Decompression can notably contribute to melting in large impacts on early Mars.•Paucity of large carters on Mars may explained by craters drowning in their melt.•Classical scaling laws fail to estimate melt production by large impactors (> 10 km).