Some members of Fiji's Great Council of chiefs are threatening to vote against President Iloilo's nomination of a new vice president if they think the choice is influenced by the military.
The chiefs, who want to remain anonymous, have told the Fiji Times that president Iloilo's choice should not be influenced by anyone.
One of these chiefs is quoted as saying that if the Great Council rejects President Iloilo's nomination, he should resign because it would a sign the chiefs no longer have confidence in him.
Fiji's prime minister, the chairman of the Great Council of Chiefs and the military commander have already met President Iloilo to discuss the nomination.
The military has strongly opposed the nomination of anyone tainted by the coup and Commodore Bainimarama has advised President Iloilo to be cautious when making his choice.
The Great Council of chiefs will begin a three-day meeting from Wednesday to vote on the vice presidency.
The official secretary to the president at the time of the coup, Joseph Browne, says the President Iloilo has the authority to make his decision on any matter, with or without outside advice.