Measurements of the W-+/- -> l(+/-) v and Z -> l(+)l(-) production cross sections (where l(+/-) = e(+/-), mu(+/-)) in proton-proton collisions at root s = 13 TeV are presented using data recorded by the ATLAS experiment at the Large Hadron Collider, corresponding to a total integrated luminosity of 81 pb(-1). The total inclusive W+-boson production cross sections times the single-lepton-flavour branching ratios are sigma(tot)(w+) = 11.83 +/- 0.02 (stat) +/- 0.32 (sys) +/- 0.25 (lumi) nb and sigma(tot)(W-) = 8.79 +/- 0.02 (stat) +/- 0.24 (sys) +/- 0.18 (lumi) nb for W+ and W-, respectively. The total inclusive Z-boson production cross section times leptonic branching ratio, within the invariant mass window 66 < m(tt) < 116 GeV, is sigma(tot)(Z) = 1.981 +/- 0.007 (stat) +/- 0.038 (sys) +/- 0.042 (lumi) nb. The W+, W-, and Z-boson production cross sections and cross-section ratios within a fiducial region defined by the detector acceptance are also measured. The cross-section ratios benefit from significant cancellation of experimental uncertainties, resulting in sigma(fid)(W+)/sigma(fid)(W-) = 1.295 +/- 0.003 (stat) +/- 0.010 (sys) and sigma(fid)(W +/-)/sigma(fid)(Z) = 10.31 +/- 0.04 (stat) +/- 0.20 (sys). Theoretical predictions, based on calculations accurate to next-to-next-to-leading order for quantum chromodynamics and to next-to-leading order for electroweak processes and which employ different parton distribution function sets, are compared to these measurements. (C) 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).