The interaction between two spherical colloids immersed in an electrolyte of screening constant kappa is studied using the recent charge regulation primitive model and the hypernetted chain integral equation. The charge of the particles is not fixed a priori but results from the adsorption of positive and/or negative ions onto the colloidal surfaces. In the case of symmetrical adsorption, the model exhibits a long-range attraction between the globally neutral colloids. At large distance, the effective colloid-colloid potential behaves as -exp(-2 kappa r)/r(2) for small colloids where r is the center to center interparticles distance and as -exp(-2 kappa h)/h for large colloids where h is the surface to surface distance. For nonsymmetrical cases, such an attraction adds to the usual screened Coulombic repulsion between the globally charged colloids. The numerical results and the physical origin of the attraction are explained in terms of elementary diagrams. The attraction arises from the ion exchange between the adsorbed layers and the bulk and from the non mean-field ion-ion correlations.