(57)Fe Mössbauer spectroscopy was applied to investigate the superconductor parent compound Fe(1+x)Te for x = 0.06, 0.10, 0.14, 0.18 within the temperature range 4.2-300 K. A spin density wave (SDW) within the iron atoms occupying regular tetrahedral sites was observed, with the square root of the mean square amplitude at 4.2 K varying between 9.7 and 15.7 T with increasing x. Three additional magnetic spectral components appeared due to the interstitial iron distributed over available sites between the Fe-Te layers. The excess iron showed hyperfine fields at approximately 16, 21 and 49 T for three respective components at 4.2 K. The component with a large field of 49 T indicated the presence of isolated iron atoms with large localized magnetic moments in interstitial positions. Magnetic ordering of the interstitial iron disappeared in accordance with the fallout of the SDW with increasing temperature.