"There is only one legal authority in the country at this time and that is the democratically elected government which I lead," he told Radio Fiji.
But he appeared to concede that his government may be finished.
"I'm 67 years old, I'm not young any more. The option of permanent retirement is also there," he said.
"There is only one legal authority in the country at this time and that is the democratically elected government which I lead"
Laisenia Qarase, deposed Fiji PM
Send us your views
The Great Council of Chiefs, the traditional authority which represents 14 chiefly provinces and appoints the president, opposed the takeover as undemocratic, illegal and disrespectful.
But Ratu Ovini Bokini, its chairman, said on Friday it would consider the army's request to have a meeting.
Bainimarama has been trying to get the council to meet to endorse the reinstatement of Ratu Josefa Iloilo as president, the first step towards naming an interim government.
An endorsement from the council would afford the new government a veneer of legitimacy.
One widely respected chief, Ratu Epeli Ganilau, has offered himself as a mediator between the military and the council.
"We all know it [the coup] is illegal but it is the lesser of two evils," said Ganilau, a former head of the military who appointed Bainimarama army chief in 1999.
But opposition to the coup remains strong.
Christian churches, which represent more than 80 per cent of indigenous Fijians, took out large newspaper advertisements on Friday to spell out their opposition to Bainimarama.
"We are deeply convinced that the move now taken by the commander and his advisers is the manifestation of darkness and evil," Reverend Tuikilakila Waqairatu, president of the Fiji Council of Churches, said in the advertisement.
Industry watchers and political observers warn that Fiji's coup is also dragging down the economy as military presence in the streets scare tourists and investors.
Airline and resort bookings feeding the Pacific island $516m-a-year tourism industry - more than half its economy - plummeted amid tensions in the months preceding the coup.
Fiji's central bank has slapped capital controls on banks and capped commercial loans to protect foreign reserves and prevent a flight of capital.
Nervous shopkeepers fear a return to the violence of the racially motivated 2000 coup, when indigenous Fijians who make up about 51 per cent of the 900,000 population burned and looted ethnic Indian-owned businesses, but Suva has remained calm.