The demand from investor Yoshiaki Murakami came a day after he launched a hostile bid of up to $235 million for control of the company.
Toshiba Machine has said it could adopt poison-pill measures to fend off acquisition attempts by issuing stock warrants to existing shareholders and diluting the holdings of unwanted suitors.
In a letter sent to the former Toshiba Corp subsidiary on Wednesday, an investment company backed by Murakami said the implementation of defense measures without shareholders' approval would be "unacceptable".
Toshiba Machine said it is examining Murakami's tender offer.
If the company decides to adopt the poison-pill defense without shareholders' approval, the Murakami side would seek a court injunction against the measures, a person with direct knowledge of the matter said.
Separately on Wednesday, BlackRock Inc said in a regulatory filing that the world's largest asset manager has built a 5.12% stake in Toshiba Machine for purely investment purposes.
(Reporting by Makiko Yamazaki; editing by Muralikumar Anantharaman and Jason Neely)