Aims. We have analyzed optical spectra of 25 X-ray sources identified as potential new members of the Taurus molecular cloud (TMC), in order to confirm their membership in this star-forming region. Methods: Fifty-seven candidate members were previously selected among the X-ray sources in the XEST survey, having a 2MASS counterpart compatible with a pre-main sequence star based on color-magnitude and color-color diagrams. We obtained high-resolution optical spectra for 7 of these candidates with the SARG spectrograph at the TNG telescope, which were used to search for lithium absorption and to measure the Hα line and the radial and rotational velocities. Then, 18 low-resolution optical spectra obtained with the instrument DOLORES for other candidate members were used for spectral classification, for Hα measurements, and to assess membership together with IR color-color and color-magnitude diagrams and additional information from the X-ray data. Results: We found that 3 sources show lithium absorption, with equivalent widths (EWs) of 500 mÅ, broad spectral line profiles, indicating rotational velocities of 20{-}40 km s-1, radial velocities consistent with those for known members, and Hα emission. Two of them are classified as new weak-lined T Tauri stars, while the EW ( -9 Å) of the Hα line and its broad asymmetric profile clearly indicate that the third star (XEST-26-062) is a classical T Tauri star. Fourteen sources observed with DOLORES are M-type stars. Fifteen sources show Hα emission. Six of them have spectra that indicate surface gravity lower than in main sequence stars, and their de-reddened positions in IR color-magnitude diagrams are consistent with their derived spectral type and with pre-main sequence models at the distance of the TMC. The K-type star XEST-11-078 is confirmed as a new member on the basis of the strength of the Hα emission line. Overall, we confirm membership to the TMC for 10 out of 25 X-ray sources observed in the optical. Three sources remain uncertain.