We study the comoving space density of X-ray-selected luminous active galactic nuclei (AGNs) and the obscured AGN fraction at high redshifts ($3 < z < 5$) in the Subaru/{it XMM-Newton} Deep Survey (SXDS) field. From an X-ray source catalog with high completeness of optical identification thanks to deep optical images, we select a sample of 30 AGNs at $z > 3$ with intrinsic (de-absorbed and rest-frame 2--10 keV) luminosities of $L_{rm X} = 10^{44-45}$ erg s$^{-1}$ detected in the 0.5--2 keV band, consisting of 20 and 10 objects with spectroscopic and photometric redshifts, respectively. Utilizing the $1/V_{rm max}$ method, we confirm that the comoving space density of luminous AGNs decreases with redshift above $z > 3$. When combined with the {it Chandra}-COSMOS result of Civano et al. (2011), the density decline of AGNs with $L_{rm X} = 10^{44-45}$ erg s$^{-1}$ is well represented by a power law of $(1 + z)^{-6.2 pm 0.9}$. We also determine the fraction of X-ray obscured AGNs with $N_{rm H} > 10^{22}$ cm$^{-2}$ in the Compton-thin population to be 0.54$^{+0.17}_{-0.19}$, by carefully taking into account observational biases including the effects of photon statistics for each source. This result is consistent with an independent determination of the type-2 AGN fraction based on optical properties, for which the fraction is found to be 0.59$pm$0.09. Comparing our result with that obtained in the local Universe, we conclude that the obscured fraction of luminous AGNs increases significantly from $z=0$ to $z>3$ by a factor of 2.5$pm$1.1.
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