We show that Stolarsky's invariance principle, known for point distributions on the Euclidean spheres, can be extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane. A part of the results (Theorem~1.1 ana Corollary~1.1) was given early in the previous paper [22], while the explicit formulas for the constants in the invariance principles for projective spaces (Theorem~1.2 and Corollary~1.2) are new.