A computational investigation of the effects of molecular topology, namely, linear and circular, as well as counterion valency, on the ensuing pairwise effective interactions between DNA molecules in an unlinked state is presented. Umbrella sampling simulations have been performed through the introduction of bias potential along a reaction coordinate defined as the distance between the centers-of-mass of pairs of DNA molecules, and effective pair interaction potentials have been computed by employing the weighted histogram analysis method. An interesting comparison can be drawn between the different DNA topologies studied here, especially with regard to the contrasting effects of divalent counterions on the effective pair potentials: while DNA-DNA repulsion in short center-of-mass distances decreases significantly in the presence of divalent counterion-ions (as compared to monovalent ions) for linear DNA, the opposite effect occurs for the DNA minicircles. This can be attributed to the fact that linear DNA fragments can easily adopt relative orientations that minimize electrostatic and steric repulsions by rotating relative to one another and by exhibiting more pronounced bending due to the presence of free ends.