Rotationally resolved molecular hydrogen transitions originating from excitation of highly excited rovibrational levels of the X^1^{SIGMA}^+^_g_ state have been systematically identified for the first time in the Far Ultraviolet Spectroscopic Explorer (FUSE) observation of comets C/2000 WM1 (LINEAR) and C/2001 A2 (LINEAR). Spectral assignments for the observed lines of H_2_ and other atomic and molecular species are given. All observed H_2_ transitions belong to the Lyman (B^1^{SIGMA}^+^_u_-X^1^{sigma}^+^_g_) and Werner (C^1^{PI}_u_-X^1^{SIGMA}^+^_g_) band systems. Resonant excitation of H_2_ by Ly{beta} and other solar lines is very limited.