The influence of vacancies and interstitial atoms on magnetism in Pu is considered in the framework of the density functional theory. The crystal structure relaxation arising due to various types of defects is calculated using the molecular dynamics method with a modified embedded atom model. The local density approximation with explicit inclusion of Coulomb and spin-orbit interactions is applied in matrix invariant form to describe correlation effects in Pu with these types of defects. The calculations show that both vacancies and interstitials give rise to local moments in the f-shell of Pu in good agreement with experimental data for aged Pu. Magnetism appears due to the destruction of a delicate balance between spin-orbit and exchange interactions.