The magnetic properties of ATcO₃ (A = Ca, Sr, Ba) perovskites were studied from first principles using multiple-scattering theory. For each system, the most preferable magnetic order is antiferromagnetic where the magnetic moments of the nearest Tc atoms are aligned antiparallel to each other. In the case of CaTcO₃ and SrTcO₃, their recently observed antiferromagnetism is supported by our calculation of the Tc-Tc exchange coupling parameters. The N´eel temperatures TN estimated for CaTcO₃ and SrTcO₃ are in a good agreement with experiment. For BaTcO₃, which is not synthesized so far, we predict a fundamental band gap of 0.3 eV and T_N below 900 K. In general, T_N increases with volume expansion, whereas the presence of vacancies on both the oxygen and cation sites of ATcO₃ should significantly suppress the critical temperature as well as the magnetic moment of Tc. Electronic correlations play a minor role in the formation of the magnetic state, although they may improve the calculated value of T_N.