We exploit XMM-Newton archival data in a study of the extended X-ray emission emanating from the Galactic Centre ( GC ) region . XMM-Newton EPIC-pn and EPIC-MOS observations , with a total exposure time approaching 0.5 and 1 Ms respectively , were used to create mosaiced images of a 100 pc \times 100 pc region centred on Sgr A* in four bands covering the 2–10 keV energy range . We have also constructed a set of narrow-band images corresponding to the neutral iron fluorescence line ( Fe i K \alpha ) at 6.4 keV and the K-shell lines at 6.7 keV and 6.9 keV from helium-like ( Fe xxv K \alpha ) and hydrogenic ( Fe xxvi Ly \alpha ) iron ions . We use a combination of spatial and spectral information to decompose the GC X-ray emission into three distinct components . These comprise : firstly the emission from hard X-ray emitting unresolved point sources ; secondly the reflected continuum and fluorescent line emission from dense molecular material ; and , thirdly , the soft diffuse emission from thermal plasma in the temperature range , kT \approx 0.8–1.5 keV . We show that the unresolved-source component accounts for the bulk of the 6.7-keV and 6.9-keV line emission and also makes a major contribution to both the 6.4-keV line emission and the 7.2–10 keV continuum flux . We fit the observed X-ray surface brightness distribution with an empirical 2-d model , which we then compare with a prediction based on an NIR-derived 3-d mass model for the old stellar population in the GC . The X-ray surface brightness falls-off more rapidly with angular offset from Sgr A* than the mass-model prediction . One interpretation is that the 2–10 keV X-ray emissivity increases from \approx 5 \times 10 ^ { 27 } erg s ^ { -1 } ~ { } \hbox { $ M _ { \odot } $ } ^ { -1 } at 20 \arcmin up to almost twice this value at 2 \arcmin . Alternatively , some refinement of the mass model may be required , although it is unclear whether this applies to the Nuclear Stellar Cluster , the Nuclear Stellar Disc , or a combination of both components . The unresolved hard X-ray emitting source population , on the basis of spectral comparisons , is most likely dominated by magnetic cataclysmic variables , primarily intermediate polars . We use the X-ray observations to set constraints on the number density of such sources at angular offsets between 2 \arcmin - 20 \arcmin from Sgr A* ( projected distances at the GC of 4.6–46 pc ) . Our analysis does not support the conjecture that a significant fraction of the hard X-ray emission from the GC originates in very-hot ( \sim 7.5 keV ) diffuse thermal plasma .