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 nonthermal 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 grand unified theory (GUT) models such as SO(10), where they can be formed at an intermediate stage of symmetry breaking well below the GUT scale ∼1016 GeV; such light strings are not excluded by the cosmic microwave background (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 ηB - L ≳ 1-7 × 1011 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 Wilkinson microwave anisotropy probe (WMAP) results, the lightest heavy right-handed Majorana neutrino mass M1 must satisfy the constraint M1 ≤ 2.4 × 1012(ηB - L/1013 GeV) 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 seesaw mechanism.