Toshiba has already announced exits from its British nuclear power and U.S. LNG businesses as part of a plan to regain investor confidence after a 2015 accounting scandal uncovered widespread irregularities and forced it to recognize huge cost overruns at its now-bankrupt U.S. nuclear unit Westinghouse.
"We believe that further firm commitments to divest other non-core businesses (such as Toshiba TEC for instance), would be well received and affirms management’s commitment to decisive execution of its plans," the investment fund said in a letter sent to Toshiba CEO Nobuaki Kurumatani and shown to Reuters.
The fund also reiterated its call for the company to boost share buybacks to 1.1 trillion yen ($901.5 million), calling its current 700 billion yen repurchase launched in November "grossly insufficient".
Toshiba had substantial excess capital, and a higher buyback would make sense "especially with the current depressed share price of Toshiba", the fund said.
It also called on the company to hire more board members with international experience.
"As a long-term shareholder of Toshiba, we may feel the need to propose an agenda item at the AGM next year should we feel that our suggestions have not been given due consideration," the fund said.
Toshiba could not immediately comment.
It was not immediately clear how much stake Argyle owned in Toshiba.
Argyle had previously opposed Toshiba's sale of its chip business to a Bain Capital-led group, saying the deal undervalued the prized unit. The sale was completed earlier this year.
(Reporting by Taro Fuse; Writing by Ritsuko Ando; Editing by Muralikumar Anantharaman)