An inclusive search for a new-physics signature of lepton-jet resonances has been performed by the ATLAS experiment. Scalar leptoquarks, pair-produced in pp collisions at root s = 13 TeV at the large hadron collider, have been considered. An integrated luminosity of 3.2 fb(-1), corresponding to the full 2015 dataset was used. First (second) generation leptoquarks were sought in events with two electrons (muons) and two or more jets. The observed event yield in each channel is consistent with Standard Model background expectations. The observed (expected) lower limits on the leptoquark mass at 95% confidence level are 1100 and 1050 GeV (1160 and 1040 GeV) for first and second generation leptoquarks, respectively, assuming a branching ratio into a charged lepton and a quark of 100%. Upper limits on the aforementioned branching ratio are also given as a function of leptoquark mass. Compared with the results of earlier ATLAS searches, the sensitivity is increased for leptoquark masses above 860 GeV, and the observed exclusion limits confirm and extend the published results.