We present long-slit H- and K-band spectroscopy of the low-mass outflow source SVS 13, obtained with the adaptive-optics-assisted imager-spectrometer NACO on the VLT. With a spatial resolution of <0farcs25 and a pixel scale of 0farcs027, we precisely establish the relative offsets of H2, [Fe II], CO, H I, and Na I components from the source continuum. The H2 and [Fe II] peaks are clearly associated with the jet, while the CO, H I, and Na I peaks are spatially unresolved and coincident with the source, as is expected for emission associated with accretion processes. The H2 profile along the slit is resolved into multiple components, which increase in size, although they decrease in intensity, with distance from the source. This trend might be consistent with thermal expansion of packets of gas ejected during periods of increased accretion activity. Indeed, for the brightest component nearest the source, proper-motion measurements indicate a tangential velocity of 0farcs028 yr-1. It therefore seems unlikely that this emission peak is associated with a stationary zone of warm gas at the base of the jet. However, the same cannot be said for the [Fe II] peak, for which we see no evidence for motion downwind, even though radial velocity measurements indicate that the emission is associated with higher jet velocities. We postulate that the [Fe II] could be associated with a collimation shock at the base of the jet.