Large-scale calculations of the E1 strength are performed within the random phase approximation (RPA) based on the relativistic point-coupling mean field approach in order to derive the radiative neutron capture cross sections for all nuclei of astrophysical interest. While the coupling to the singleparticle continuum is taken into account in an explicit and self-consistent way, additional corrections like the coupling to complex configurations and the temperature and deformation effects are included in a phenomenological way to account for a complete description of the nuclear dynamical problem. It is shown that the resulting E1-strength function based on the PCF1 force is in close agreement with photoabsorption data as well as the available experimental E1 strength data at low energies. For neutron-rich nuclei, as well as light neutron-deficient nuclei, a low-lying so-called pygmy resonance is found systematically in the 5-10 MeV region. The corresponding strength can reach 10% of the giant dipole strength in the neutron-rich region and about 5% in the neutron-deficient region, and is found to be reduced in the vicinity of the shell closures. Finally, the neutron capture reaction rates of neutron-rich nuclei is found to be about 2-5 times larger than those predicted on the basis of the nonrelativistic RPA calculation and about a factor 50 larger than obtained with traditional Lorentzian-type approaches.