The kinetic description of relativistic plasmas in the presence of time-varying and spatially non-uniform electromagnetic (EM) fields is a fundamental theoretical issue both in astrophysics and plasma physics. This refers, in particular, to the treatmentof collisionless and strongly-magnetized plasmas in the presence of intense radiation sources. In this paper, the problem is investigated in the framework of a covariant gyrokinetic treatment for Vlasov-Maxwell equilibria. The existence of a new class of kinetic equilibria is pointed out, which occur for spatially-symmetric systems. These equilibria are shown to exist in the presence of non-uniform background EM fields and curved space-time. In the non-relativistic limit, this feature permits the determination of kinetic equilibria even for plasmas in which particle energy is not conserved due to the occurrence of explicitly time-dependent EM fields. Finally, absolute stability criteria are established which apply in the case of infini