In this article we prove the backward uniqueness (as well as the uniqueness) for a class, defined in the article, of solutions of the two-dimensional primitive equations that we call z-weak solutions.We also prove the backward uniqueness for the strong solutions in the two- and three-dimensional cases. By backward uniqueness we understand that once we know that two solutions are equal at a time t > 0, then we can conclude that they are equal everywhere on the interval (0, t).