The Great Council of Chiefs in Fiji says the pairing of President Iloilo and Vice President Madraiwiwi will keep the country stable in the event the government changes after a general election in May.
President Iloilo was firs appointed head of state in July 2000 after the coup.
His deputy Ratu Jope Seniloli, was replaced last year after being jailed for trying to usurp the presidency during the coup.
The general secretary of the Great Council, Asesala Sadole, says in their decision, the chiefs acknowledged the potential of Vice President Madraiwiwi to assume the presidency in the future.
"They were thinking of the stability of this country and they were unanimously elected for another term. They have served this country well for the last - for Ratu Josefa Iloilo - for the last five years, and for Ratu Jone Madraiwiwi for the last year, because he has been replacing Ratu Jope Seniloli; and I think they were doing a very good job."
Mr Sadole says the chiefs considered Ratu Josefa Iloilo, to be in good enough health to stay in office.
Ratu Josefa is 85 and has been sent for medical treatment abroad several times in recent years.