The absorption edge of GaN_xP_1-x alloys (0.01<=x<=0.03) is shown to exhibit a direct-band gap-like behavior. Thermal variation of the band gap energy Eg, however, is found to be the same or even smaller than that for the indirect band gap of GaP and depends on the N content. The effect is tentatively attributed to the following counteracting contributions to the band edge formation. An interaction with N-related localized states, especially significant in the vicinity of band crossover (e.g., x = 0.013), causes a substantial slow down of the E_g shift with temperature. On the contrary, an increasing contribution of Γ_c states, which becomes predominant for the higher compositions, leads to the larger thermal variation in E_g.