[en] We discuss the results of two XMM-Newton observations of the open cluster NGC 6604 obtained in April and September 2002. We concentrate mainly on the multiple system HD 167971 (O5- 8V + O5- 8V + (O8I)). The soft part of the EPIC spectrum of this system is thermal with typical temperatures of about 2 x 106 to 9 x 106 K. The nature ( thermal vs. non-thermal) of the hard part of the spectrum is not unambiguously revealed by our data. If the emission is thermal, the high temperature of the plasma (similar to 2.3 x 10(7) to 4.6 x 10(7) K) would be typical of what should be expected from a wind-wind interaction zone within a long period binary system. This emission could arise from an interaction between the combined winds of the O5- 8V + O5- 8V close binary system and that of the more distant O8I companion. Assuming instead that the hard part of the spectrum is non-thermal, the photon index would be rather steep (similar to 3). Moreover, a marginal variability between our two XMM-Newton pointings could be attributed to an eclipse of the O5 - 8V + O5 - 8V system. The overall X-ray luminosity points to a significant X-ray luminosity excess of about a factor 4 possibly due to colliding winds. Considering HD 167971 along with several recent X-ray and radio observations, we propose that the simultaneous observation of non-thermal radiation in the X-ray (below 10.0 keV) and radio domains appears rather unlikely. Our investigation of our XMM-Newton data of NGC 6604 reveals a rather sparse distribution of X-ray emitters. Including the two bright non-thermal radio emitters HD 168112 and HD 167971, we present a list of 31 X-ray sources along with the results of the cross-correlation with optical and infrared catalogues. A more complete spectral analysis is presented for the brightest X-ray sources. Some of the members of NGC 6604 present some characteristics suggesting they may be pre-main sequence star candidates.