X-ray single-grating interferometry was applied to conduct accurate wavefront corrections for hard X-ray nanofocusing mirrors. Systematic errors in the interferometer, originating from a grating, a detector, and alignment errors of the components, were carefully examined. Based on the measured wavefront errors, the mirror shapes were directly corrected using a differential deposition technique. The corrected X-ray focusing mirrors with a numerical aperture of 0.01 attained two-dimensionally diffraction-limited performance. The results of the correction indicate that the uncertainty of the wavefront measurement was less than λ/72 in root-mean-square value.