The invention describes improved mortar compositions that can reach compressive strength values up to six times more than the obtained ones by conventional mortars at the first hours of setting, as well as up to three times more at 28 days of setting. Cementitious materials, such as Portland cement and clinker of Portland cement were refined in a high energy mill until reaching the greater fineness possible (100%<10,um) to obtain a material with greater mechanical resistance by compression that those that are reached with normal cement. The compositions of the invention containing the refined cementitious material as well as refined and suitably distributed sand, develop compressive strengths substantially higher (greater to 100 MPa).