We consider a temporal response of relativistically broadened line spectrum of iron from black hole accretion irradiated by an X-ray echo under strong gravity. The physical condition of accreting gas is numerically calculated in the context of general relativistic hydrodynamics under steady-state, axisymmetry in Kerr geometry. With the onset of a point-like X-ray flare of a short finite duration just above the accretion surface, the gas is assumed to be ionized to produce a neutral iron fluorescent line. Using a fully relativistic ray-tracing approach, the response of line photons due to the X-ray illumination is traced as a function of time and energy for different source configurations around Schwarzschild and Kerr black holes. Our calculations show that the X-ray echo on the accretion surface clearly imprints a characteristic time-variability in the line spectral features depending on those parameters. Simulated line profiles, aimed for the future microcalorimeter missions of large collecting area such as Athena/X-IFU for typical radio-quiet Seyfert galaxies, are presented to demonstrate that state-of-the-art new observations could differentiate various source parameters by such an X-ray tomographic line reverberation.