In this study we present the experimental differential cross sections of natO(p,p0) elastic scattering, determined via the relative measurement technique, in the proton beam energy range Elab=4-6 MeV with a varying step (from 5-15 keV), at six backscattering detector angles between 120o and 170o (every 10o). A thin, self-supporting target manufactured in the lab was used in this experiment and the determination of its stoichiometry was carried out according to the currently existing evaluation, which has also been benchmarked recently. The measurements were performed using the Van de Graaff Tandem 5.5 MV Accelerator of N.C.S.R. “Demokritos” in Athens, Greece. The differential cross-section datasets obtained in the present work and already existing ones in literature for this extended proton beam energy range are shown and the observed peculiarities and discrepancies are discussed and analyzed.