We report on electron spin resonance studies of H atoms stabilized in solid H \(_{2}\) films at temperature 0.7 K and in a magnetic field of 4.6 T. The H atoms were produced by bombarding H \(_{2}\) films with 100 eV electrons from a radiofrequency discharge run in the sample cell. We observed a one order of magnitude faster H atom accumulation in the films made of para-H \(_{2}\) gas with a small ortho-H \(_{2}\) concentration (0.2% ortho-H \(_{2}\) ) as compared with those made from normal H \(_{2}\) gas content (75% ortho-H \(_{2}\) ). We also studied the influence of ortho-H \(_{2}\) molecules on spatial diffusion of H atoms in solid H \(_{2}\) films. The spatial diffusion of H atoms in both normal and para-H \(_{2}\) films is faster than the diffusion obtained from the measurement of H atom recombination. The rate of spatial diffusion of H atoms in para-H \(_{2}\) films was slower in comparison with that in the normal H \(_{2}\) films. We discuss possible explanations of these observations.