The mean force and the potential of the mean force between two like-charged macroions with monovalent counterions and added simple 1:3 salt described within the primitive model and confined in a cylindrical cell have been investigated by Monte Carlo simulations. Without additional salt, a strongly repulsive mean force was obtained at all macroion separations, consistent with a stable solution of macroions. At a trivalent counterion-to-macroion charge ratio of 0.4, the mean force became attractive at short separations but still possessed a substantial repulsion at longer separations. However, at a stoichiometric amount of trivalent counterions, no long-range repulsion remained and the attraction became substantial (approximate to5kT attraction at a short separation). In excess of salt, the magnitude of the attractive mean force was reduced. The attractive component of the mean force originates from spatial correlations between counterions residing near different macroions and is not captured by mean-field theories such as the Poisson-Boltzmann equation or any of its simplifications. The observed sequence of mean forces is consistent with recent experimental observations on an aqueous solution of sodium dodecyl sulfate micelles as Al(NO3)(3) was added.