We present the results obtained from the analysis of three XMM-Newton observations of M83. The aims of the paper are studying the X-ray source populations in M83 and calculating the X-ray luminosity functions of X-ray binaries for different regions of the galaxy. We detected 189 sources in the XMM-Newton field of view in the energy range of 0.2-12 keV. We constrained their nature by means of spectral analysis, hardness ratios, studies of the X-ray variability, and cross-correlations with catalogues in X-ray, optical, infrared, and radio wavelengths. We identified and classified 12 background objects, five foreground stars, two X-ray binaries, one supernova remnant candidate, one super-soft source candidate and one ultra-luminous X-ray source. Among these sources, we classified for the first time three active galactic nuclei (AGN) candidates. We derived X-ray luminosity functions of the X-ray sources in M83 in the 2-10 keV energy range, within and outside the D_25 ellipse, correcting the total X-ray luminosity function for incompleteness and subtracting the AGN contribution. The X-ray luminosity function inside the D_25 ellipse is consistent with that previously observed by Chandra. The Kolmogorov-Smirnov test shows that the X-ray luminosity function of the outer disc and the AGN luminosity distribution are uncorrelated with a probability of about 99.3%. We also found that the X-ray sources detected outside the D_25 ellipse and the uniform spatial distribution of AGNs are spatially uncorrelated with a significance of 99.5%. We interpret these results as an indication that part of the observed X-ray sources are X-ray binaries in the outer disc of M83.
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