In this work we present a systematic study of the magnetic interactions within 3d transition-metal chains adsorbed on Cu2N and Cu2O monolayers grown on Cu(001). We are interested in the particular geometric adsorption configuration which gives rise, after relaxation, to the development of diatomic TM-X (X = N, O) chains. By using density functional theory (DFT), we calculate the energy difference between the ferromagnetic and antiferromagnetic intrachain configurations for Ti, V, Cr, Mn, Fe, and Co. Both substrates give rise, with minor differences, to the same magnetic trends, the only chains which are ferromagnetic after adsorption are Cr chains. By performing similar calculations in unsupported chains and introducing a tight-binding-model Hamiltonian based on physically reasonable assumptions we reproduce the magnetic trends obtained from the DFT calculations.