To establish the nature of cometary X-ray emissions above 1 keV, detailed modeling of scattering and fluorescence of solar X-rays by a cometary atmosphere is carried out over the 0.3-3.0 keV photon energy range. Computations of the X-ray emissions are performed for different distributions of the cometary neutral gas, dust, and ice grains, with an emphasis placed on nano-sized particles. The calculated emission spectra of energetic photons above 1 keV are compared to cometary observations performed by the Chandra X-ray Observatory, and emission contributions solely from cometary neutral gas are found to be an insufficient X-ray production mechanism. Further comparison between the developed model and observational data also establishes an upper limit on dust and ice nanoparticle density distributions in cometary atmospheres. In addition, similarities in spectral shape above 1 keV observed between cometary emissions, Jovian disk emissions, and scattered solar X-ray spectra during solar flare events are discussed in detail.