Results are presented on event-by-event fluctuations in transverse momentum of charged particles, produced at forward rapidities in p+p, C+C, Si+Si, and Pb+Pb collisions at 158 AGeV. Three different characteristics are discussed: the average transverse momentum of the event, the ΦpT fluctuation measure, and two-particle transverse momentum correlations. In the kinematic region explored, the dynamical fluctuations are found to be small. However, a significant system size dependence of ΦpT is observed, with the largest value measured in peripheral Pb+Pb interactions. The data are compared with predictions of several models.