The statement marks the first time that Singapore-based Effissimo has made its views known since a shareholder-commissioned investigation revealed Toshiba colluded with the Japanese government to block foreign shareholders from having influence.
Effissimo, which holds about 10% of Toshiba's shares, said the board's decision to remove only two board director nominees in response to the investigation was a reminder that it was unwilling to hold the board members accountable.
Toshiba was not immediately available for comment.
Shareholder advisory groups Institutional Shareholder Services Inc and Glass Lewis continue to recommend that shareholders should vote against the re-appointment of Board Chairman Osamu Nagayama and certain other current directors.
3D Investment Partners, Toshiba's second-largest shareholder, has also called for the resignation of Nagayama.
Effissimo's statement, first reported by the Financial Times, did not call for a resignation of specific directors, but said it would "continue to hold the board members accountable when necessary."
The independent investigation last week alleged that the company's management colluded with Japan's trade ministry to prevent foreign investors from gaining board influence, in what 3D Investment called the world's worst corporate scandal in a decade.
(Reporting by Makiko Yamazaki in Tokyo and Chavi Mehta in Bengaluru; Editing by Maju Samuel and Jane Merriman)
By Makiko Yamazaki and Chavi Mehta