Cosmic strings arising from breaking of the U ( 1 ) _ { B - L } gauge symmetry that occurs in a wide variety of unified models can carry zero modes of heavy Majorana neutrinos . Decaying and/or repeatedly self-interacting closed loops of these “ B - L ” cosmic strings can be a non-thermal source of heavy right-handed Majorana neutrinos whose decay can contribute to the observed baryon asymmetry of the Universe ( BAU ) via the leptogenesis route . The B - L cosmic strings are expected in GUT models such as SO ( 10 ) , where they can be formed at an intermediate stage of symmetry breaking well below the GUT scale \sim 10 ^ { 16 } GeV ; such light strings are not excluded by the CMB anisotropy data and may well exist . We estimate the contribution of B - L cosmic string loops to the baryon-to-photon ratio of the Universe in the light of current knowledge on neutrino masses and mixings implied by atmospheric and solar neutrino measurements . We find that B - L cosmic string loops can contribute significantly to the BAU for U ( 1 ) _ { B - L } symmetry breaking scale \eta _ { B - L } \mbox { \raisebox { -2.58 pt } { ~ { } $ \stackrel { > } { \sim } $~ { } } } 1.7 \times 10 ^ { 1 % 1 } { GeV } . At the same time , in order for the contribution of decaying B - L cosmic string loops not to exceed the observed baryon-to-photon ratio inferred from the recent WMAP results , the lightest heavy right-handed Majorana neutrino mass M _ { 1 } must satisfy the constraint M _ { 1 } \leq 2.4 \times 10 ^ { 12 } \left ( \eta _ { B - L } / 10 ^ { 13 } { GeV } \right ) ^ { 1 / 2 } { % GeV } . This may have interesting implications for the associated Yukawa couplings in the heavy neutrino sector and consequently for the light neutrino masses generated through see-saw mechanism .