Accurate QED evaluations of the one- and two-photon interelectron interaction for low-lying two- and three-electron configurations for ions with nuclear charge numbers 60less than or equal toZless than or equal to93 are performed. The three-photon interaction is also partly taken into account. The Coulomb gauge is employed. The results are compared with available experimental data and with different calculations. A detailed investigation of the behavior of the energy levels of the configurations 1s(1/2)2s(1/2)1S(0), 1s(1/2)2p(1/2)3P(0) near Z=64 and Z=92 is carried out. The knowledge of the exact energy difference near these regions is important for the future experimental search for parity nonconserving effects in highly charged ions.