The micromechanical damage model has been developed to better describe multiscale fracture behavior in quasi-brittle rocks. While the deduced yield criterion under tension and compression has been carefully investigated in different stress spaces, it fails to capture a smooth transition from extension to shear fracture and overestimates the tensile strength of the rock. This paper introduces a unified nonlinear yield criterion based on a stress-dependent fracture energy parameter. In particular, the effect of the intermediate principal stress is encapsulated. The proposed yield criterion is then validated in the principal stress space based on a detailed parameter calibration procedure. Subsequently, four verification examples corresponding to Beishan granite, Lac du Bonnect granite, Carrara marble and Berea sandstone are carried out to show a desirable predictive capacity of the proposed yield criterion on progressive failure, extension to compressive-shear fracture transition and fault slip in quasi-brittle rocks.