Based on the full-potential linearized augmented plane-wave method combined with the generalized gradient approximation, we determine the ground-state spin configurations and the total energies of 3d transition-metal monolayer and bilayer films on Fe͑001͒ within the c(2ϫ2) unit cell. We find by energy analysis that V, Cr, and Mn layers prefer the layered antiferromagnetic coupling, and Fe, Co, and Ni layers favor the ferromagnetic coupling to Fe͑001͒. One exception is the Mn monolayer, which favors the c(2ϫ2) ferrimagnetic superstructure. We discuss the stability of the 3d transition-metal monolayer films on Fe͑001͒ against the bilayer formation and find that, with the exception of Cr, all 3d monolayers on Fe͑001͒ are stable against bilayer formation. We have confirmed that the interlayer relaxations do not change the overall features of the present results.