[en] The density dependence of nuclear symmetry energy is studied within the covariant density functional (CDF) theory in terms of the kinetic energy, isospin-singlet, and isospin-triplet potential energy parts of the energy density functional. When the Fock diagram is introduced, it is found that both isospin-singlet and isospin-triplet components of the potential energy play an important role in determining the symmetry energy. At high densities, a strong density-dependent behavior is revealed in the isospin-triplet potential part of the symmetry energy. In addition, the inclusion of the Fock terms in the CDF theory reduces the kinetic part of the symmetry energy and may lead to negative values at the supranuclear density region, which is regarded partly as the effect of the nuclear tensor-force components. The results demonstrate the importance of the Fock diagram in the CDF theory on the isospin properties of the in-medium nuclear force at high densities, especially from the isoscalar-meson coupling channels. (paper)