We present a new measurement of the space density of high redshift (3.0<z<4.5), X-ray selected QSOs obtained by exploiting the deep and uniform multiwavelength coverage of the COSMOS survey. We have assembled a statistically large (40 objects), X-ray selected (F_{0.5-2 keV} >10^{-15} cgs), homogeneous sample of z>3 QSOs for which spectroscopic (22) or photometric (18) redshifts are available. We present the optical (color-color diagrams) and X-ray properties, the number counts and space densities of the z>3 X-ray selected quasars population and compare our findings with previous works and model predictions. We find that the optical properties of X-ray selected quasars are not significantly different from those of optically selected samples. There is evidence for substantial X-ray absorption (logN_H>23 cm^{-2}) in about 20% of the sources in the sample. The comoving space density of luminous (L_X >10^{44} erg s^-1) QSOs declines exponentially (by an e--folding per unit redshift) in the z=3.0-4.5 range, with a behavior similar to that observed for optically bright unobscured QSOs selected in large area optical surveys. Prospects for future, large and deep X-ray surveys are also discussed.
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