The magnetic-dipole transition probabilities between the fine-structure levels (1 s2 2 s2 2p) P 1/2 2 - P 3/2 2 for B-like ions and (1 s2 2s2p) P13 - P23 for Be-like ions are calculated. The configuration-interaction method in the Dirac-Fock-Sturm basis is employed for the evaluation of the interelectronic-interaction correction with negative-continuum spectrum being taken into account. The 1/Z interelectronic-interaction contribution is derived within a rigorous QED approach employing the two-time Green function method. The one-electron QED correction is evaluated within framework of the anomalous magnetic-moment approximation. A comparison with the theoretical results of other authors and with available experimental data is presented.