The general secretary of the Fijian Political Party, SVT, is accusing the government of a cover up following the police commissioner's omission from the National Security Council meeting.
Ema Druavesi says the police commission, Andrew Hughes, is from overseas and so was purposefully not invited to Monday's meeting.
Ms Druavesi says it is an issue of public concern, when the police commissioner is not invited to advise the council on security risks.
"The concern of the public at large was that the government didn't intentionally want to include him was because of the fact of the involvement of some of the government's ministers and senators in the coup of 2000."
Ema Druavesi is calling for the terms of reference from the government for the inquiry.
She says the inquiry should be conducted like a public hearing, for transparency reasons.
Meanwhile, a newspaper report says Commodore Bainimarama could be asked to step aside once the commission begins its work.
The Daily Post quotes a senior government official as saying that it would only be fair that the commander go on leave while he is being investigated, as was the case with the former police commissioner, Col Isikia Savua, when he was investigated.
The official, who did not wish to be named, says sending Commodore Bainimarama on leave is one of the matters under consideration.