TOKYO, Sept 24 (Reuters) - Japan's Sumitomo Mitsui Trust Bank said on Thursday it had found about 3.4 million uncounted shareholder votes at 975 clients, after revelations of a botched count at Toshiba Corp's annual meeting.

Sumitomo Mitsui, entrusted to count votes for Japanese companies' shareholder meetings, said last week it mistakenly omitted some votes from a final tally at a Toshiba shareholder meeting.

While Toshiba and Sumitomo Mitsui have said the error did not affect the outcome of the meeting, it raised fresh questions about Japan's corporate governance, with foreign and minority investors increasingly demanding to be heard. (Reporting by Takashi Umekawa Editing by Chang-Ran Kim)