We investigate the effect of uniaxial compressions on the zero-phonon luminescence and absorption spectra of the nitrogen-bound excitons in GaP. All data have been collected at pumped-liquid-helium temperature for the stress directions , , and , respectively. The low-stress behavior of the exciton states is consistent with the simple j-j coupling scheme for the excitons, and the stress-induced splitting of the bound hole is found isotropic. The high-stress behavior is quantitatively consistent with an exciton wave function primarily associated with the <100> conduction-band minima. The corresponding valley-orbit splitting is E12=24 meV. Under stress, the valley-orbit coupling matrix element appears to be stress dependent. We find Δ=(8+4×10-4X) meV. This result clearly shows that the nitrogen potential is also stress dependent. On the other hand, since the stress dependence of the exciton binding energy Eb cannot be accounted for by a combined X-L nature of the bound-electron wave function, it results from the stress dependence of the potential extension via the stress dependence of the valley-orbit coupling matrix element.