Did the Buddha teach mantra meditation? I don´t think so.
Why? A mantra its one of many games where u lock the mind in some specific task to create a hindrance free zone by means of narrowing your field of perception-cognition-experience (u could do the same thing counting sheeps, staring at one object for long periods of time , so on..and this was very explored before the Buddha). Actually its quite amazing the similarity between that and a man who bury his problems watching tv, he could easily say: I feel better now, my mind its pure, my concentration in the movie its really good. At the end you are developing an ability to close yourself, but when u come out hindrances reappear...its the opposite of opening yourself, accepting reality, letting go hindrances instead of bury them..