We study the two-dimensional surface brightness distribution of the Galactic X-ray background emission outside the central degree around Sgr A* in the 6.7-keV line as measured by the Proportional Counter Array spectrometer of the Rossi X-ray Timing Explorer observatory. The use of the emission line instead of continuum (3–20 keV) radiation and application of time-variability filtering to the long data set allows us to strongly suppress the contamination of the Galactic ridge X-ray emission (GRXE) map by bright point-sources. The surface brightness in the 6.7-keV line demonstrates very good correspondence with the near-infrared surface brightness over the whole Galaxy, supporting the notion that the GRXE consists mostly of integrated emission from weak Galactic X-ray sources. We find compatible linear correlations between near-infrared and 6.7-keV surface brightness for the bulge and disc of the Galaxy. This indicates that the populations of weak X-ray sources making up the GRXE in the disc and in the bulge are not significantly different.