We evaluate the characteristics of a higher-order harmonics light as a seed X-ray amplified through a laser-produced X-ray amplifier. The narrow spectral bandwidth of the X-ray amplifier works as the frequency filter of the seed X-ray, resulting in that only the temporally coherent X-ray is amplified. Experimental investigation using the 29th-order harmonic light of the Ti:sapphire laser at a wavelength of 26.9 nm together with a neon-like manganese X-ray laser medium shows evident spectral narrowing of the seed X-ray and amplification without serious diffraction effects on the propagation of the amplified X-ray beam. This implies that the present combination is potential to realize temporally coherent X-ray lasers, with an expected duration of approximately 400 fs.