Carbide-based fuel assembly includes outer structural member of ceramic matrix composite material (e.g., SiC—SiC composite), insulation layer of porous refractory ceramic material (e.g., zirconium carbide with open-cell foam structure or fibrous zirconium carbide), and interior structural member of refractory ceramic-graphite composite material (e.g., zirconium carbide-graphite or niobium carbide-graphite). Spacer structures between various layers provide a defined and controlled spacing relationship. A fuel element bundle positioned between support meshes includes a plurality of distributively arranged fuel elements or a solid, unitary fuel element with coolant channels, each having a fuel composition including high assay, low enriched uranium (HALEU). Fuel assemblies are distributively arranged in a moderator block and the upper end of the outer structural member is attached to a metallic inlet tube for hydrogen propellant and the lower end of the outer structural member is interfaced with a support plate, forming a NTP reactor.