Southeastern Asset Management, the largest non-Japanese investor in Olympus, said the maker of medical optics and cameras should publish minutes of board meetings related to a series of controversial payments made during a string of acquisitions.

Southeastern said in a letter, written on October 20 but made public on Monday, it wanted to review minutes from meetings which preceded and followed the takeovers of Gyrus, Altis, Humalabo and News Chef and a number of abnormally large payments made to financial advisors as part of the transactions.

Olympus has a storied history in imaging and a high quality medical franchise that is worth significantly more than the share price, Southeastern said in the letter addressed to former Chairman and Chief Executive Tsuyoshi Kikukawa, who resigned from his post on Wednesday.

Your duty to the company and all stakeholders requires that corporate governance and management match this quality and history, the letter continued.

Executives at Olympus are struggling to convince shareholders it acted properly in paying a record $687 million (428 million pound) in advisory fees to two obscure firms related to the $2 billion acquisition of British medical equipment maker Gyrus in 2008.

The scandal, which has reignited debate about the quality of corporate governance in Japan, erupted when Olympus fired ex-CEO Michael Woodford on October 14 in what he has described as a boardroom coup sparked by his persistent questions about the payments.

They can release the board minutes; this week or tomorrow and it could make a lot of these questions go away, Josh Shores, a principal at Southeastern Asset Management said.

We have requested them, they said no on technical grounds that they couldn't just give them to us, to which we said we didn't want them exclusively -- they should be given to everybody. But they just said no, he said.

Japanese Prime Minister Yoshihiko Noda has risked the ire of politicians and the private sector by calling on Olympus to clarify the payments, citing worries about Japan's reputation as a rules-based market company, the Financial Times reported on Sunday.

In his first press conference in charge of the 92-year old company, Shuichi Takayama defended all four takeovers and the payments involved as part of an ambitious corporate strategy to reduce over-reliance on the endoscope business.

In Monday's letter, Southeastern reiterated calls for an independent audit of Olympus's financial affairs to answer questions about the acquisitions including whether the advisors were in any way affiliated to Olympus.

Southeastern also wants to know why Woodford, who told Reuters on Friday he has met with U.S. federal prosecutors, was not allowed a hearing at the final board meeting and why the company is yet to commit to the appointment of a third-party auditor to oversee the investigation.

The concern is that a committee is coming, but it is not going to be a good committee, Shores said, explaining the fund manager's reasons for making the private correspondence public.

The make-up of the committee is absolutely critical. We are just trying to keep the integrity of the committee such that when the answers come out, we can all trust them, he added.

(Reporting by Tommy Wilkes and Sinead Cruise; Editing by Jon Loades-Carter)