Résumé : IceTop is an air-shower array located on the Antarctic ice sheet at the geographic South Pole. IceTop can detect an astrophysical flux of neutrons from Galactic sources as an excess of cosmic-ray air showers arriving from the source direction. Neutrons are undeflected by the Galactic magnetic field and can typically travel 10 (E/PeV) pc before decay. Two searches are performed using 4 yr of the IceTop data set to look for a statistically significant excess of events with energies above 10 PeV (1016 eV) arriving within a small solid angle. The all-sky search method covers from -90° to approximately -50° in declination. No significant excess is found. A targeted search is also performed, looking for significant correlation with candidate sources in different target sets. This search uses a higher-energy cut (100 PeV) since most target objects lie beyond 1 kpc. The target sets include pulsars with confirmed TeV energy photon fluxes and high-mass X-ray binaries. No significant correlation is found for any target set. Flux upper limits are determined for both searches, which can constrain Galactic neutron sources and production scenarios.