The Fiji police say they cannot comment on whether investigations of the Prime Minister's actions will be completed before the election promised for September.
The two complaints, alleging that Rear Admiral Frank Bainimarama breached a decree and a law, were lodged by Mick Beddoes of the United Front for a Democratic Fiji.
The first complaint was lodged with police six weeks ago, saying the regime leader was campaigning without having his party registered, which is in breach of the Political Parties Decree.
The second complaint, that Rear Admiral Bainimarama used the coat of arms on his campaign bus in contravention of the Coat of Arms of Fiji Act, was lodged about a month ago.
The police say they cannot say how long the investigations will take.
If convicted, Rear Admiral Bainimarama could face up to 10 years in jail and would not be able to stand in the election.
Two former prime ministers, who were expected to be his main rivals, are barred from contesting the September election because of convictions for financial crimes.