This study investigates the solidus and near-solidus phase relations of a Martian model mantle composition over the pressure range of 1--3 GPa and 775--1000¿C. The presence of H2O has a tremendous effect on the solidus temperature of the Martian mantle, which decreases from 975¿C at 1 GPa down to 800¿C at 3 GPa. We use the results of this experimental investigation to explore the consequences of a wet accretion scenario for the planet Mars. The presence of H2O in accreted materials may profoundly modify the characteristics of planetary differentiation. Serpentine minerals contained in accreted materials are expected to lose most of their H2O through a series of dehydration reactions, thereby triggering massive degassing events. The vapor-saturated solidus is expected to be crossed during accretion, as the temperature of the growing planetesimal is increasing. Hydrous melting processes will contribute to early crust formation and the development of the atmosphere and hydrosphere during early Noachian. Early wet melting events during accretion might produce mantle heterogeneities (residual depleted mantle and enriched "crustal" component) that could be reprocessed during late volcanism as the sources for SNC meteorites. Experimental phase relations also predict that hydrous silicates can be buried deep into the planet, where H2O can be stored in "nominally anhydrous minerals" or in the metallic core. It is thus likely that at least some H2O has been buried in the Martian interior during accretion, with important consequences on geophysical properties during subsequent planetary evolution.