In laser welding, typical welding penetration depths are in the order of 1-2 mm/kW laser power. The multipass laser welding technique, based on the narrow-gap approach, is an emerging welding technology that can be applied to thick-section welds by using relatively low laser power, but the process is more complicated since it is necessary to introduce filler wire to narrow-gap weld configurations. The aim of this work was to understand significant process parameters and their interactions in order to control the weld quality in ultra-narrow-gap (1.5 mm gap width) laser welding of AISI grade 316L stainless steel. A 1-kW IPG single-mode fiber laser was used for welding plates that were 5 to 20 mm in thickness using the multiple-pass narrow-gap approach. Design of experiments and statistical modelling techniques were employed to understand and optimise the processing parameters. The effects of laser power, wire feed rate, and welding speed on the weld homogeneity, integrity, bead shape, gap bridgability and surface oxidation were studied. The results were evaluated under different optimising constraints. The results show that the models developed in this work can effectively predict the responses within the factors domain.