Fiji's military has refused to accept a presidential decision to oust its commander, following his threats against the government.
The Republic of Fiji Military Forces (RFMF) has said the Suva exercises are not threatening, another Fiji online media service reported.
"The RFMF has confirmed that it is conducting exercises at the Queen Elizabeth Barracks and in the greater Suva area and there is no cause for alarm," the fijivillage.com website said.
Fiji Police Commissioner Andrew Hughes, an Australian, has said police are worried about Bainimarama's outbursts against the government - so worried that he has withheld an ammunition shipment intended for the army.
Fiji has suffered three coups and a failed mutiny since 1987.
The coups have been racially fuelled, with indigenous Fijians fearful of losing political control of their island nation to ethnic Indian Fijians, who dominate the sugar and tourism-based economy.