We carried out extended spectroscopic confirmations of Lyα emitters (LAEs) at z = 6.5 and 5.7 in the Subaru Deep Field. Now, the total number of spectroscopically confirmed LAEs is 45 and 54 at z = 6.5 and 5.7, respectively, and at least 81% (70%) of our photometric candidates at z = 6.5 (5.7) have been spectroscopically identified as real LAEs. We made careful measurements of the Lyα luminosity, both photometrically and spectroscopically, to accurately determine the Lyα and rest-UV luminosity functions (LFs). The substantially improved evaluation of the Lyα LF at z = 6.5 shows an apparent deficit from z = 5.7 at least at the bright end, and a possible decline even at the faint end, though small uncertainties remain. The rest-UV LFs at z = 6.5 and 5.7 are in good agreement, at least at the bright end, in clear contrast to the differences seen in the Lyα LF. These results imply an increase in the neutral fraction of the intergalactic medium from z = 5.7 to 6.5. The rest-frame equivalent width (EW0) distribution at z = 6.5 seems to be systematically smaller than z = 5.7, and it shows an extended tail toward larger EW0. The bright end of the rest-UV LF can be reproduced from the observed Lyα LF and a reasonable EW0-UV luminosity relation. Integrating this rest-UV LF provides the first measurement of the contribution of LAEs to the photon budget required for reionization. The derived UV LF suggests that the fractional contribution of LAEs to the photon budget among Lyman break galaxies significantly increases toward faint magnitudes. Low-luminosity LAEs could dominate the ionizing photon budget, though this inference depends strongly on the uncertain faint-end slope of the Lyα LF. © 2011. The American Astronomical Society. All rights reserved.