One-dimensional transition-metal (TM) nanowires of single atom width can be formed on a stepped Cu(111) surface, as pointed out by Mo [Phys. Rev. Lett. 94, 155503 (2005)] for Fe on Cu(111). The basic template is an embedded Fe chain at one-atom distance away from the upper edge of the monatomic surface step. Chains, consisting of 3d TM atoms from Sc to Ni can be formed on top of the Fe chain. Density-functional theory is applied to calculate the magnetic ground state and to describe the magnetic properties of such TM-Fe wires. The wires form different magnetic structures but are all characterized by a high local magnetic moment.