For a two-dimensional quasi-stadium laser diode, we demonstrate stable excitation of the lowest-order transverse ring modes by optimally designing the confocal end mirrors of the laser cavity based on extended Fox-Li mode calculations. We observe kink-free light output versus injection current characteristics and highly directional single-peak emissions corresponding to the diamond-shaped trajectory in the cavity. These results provide convincing evidence for selective excitation of the lowest-order transverse modes.