A printing press for digital printing on three-dimensional objects includes a plurality of printing stations arranged in a specified radian on an outer peripheral edge of a press wheel. Each one of the printing stations includes an inkjet print head for digital printing on three-dimensional objects and a rotary table for holding the three-dimensional object. A printing unit prints on the three-dimensional object by separate printing of a mark or a logo executed as a pad print. The printing unit includes a mechanical feed unit and a plurality of pads successively arranged on a rotating wheel. The pads and the surfaces of the printed three-dimensional objects held in the printing stations are held in the same radian and move at the same circumferential speed so that the pads print on the three-dimensional objects by means of a tampograph.