Fiji's Conservative Alliance Matanitu Vanua party is threatening to walk out of the coalition government if its demand of an early release for nine men convicted of involvement in the coup, is not met.
Party spokesman and MP, Josateki Vula, says the Attorney General, Qoriniasi Bale, rejected the appeal on the grounds of national security.
But, the MP says the nine men have changed following the coup of May 2000 and they should be let go.
Mr Vula says if the decision isn't changed, the party will discuss it at caucus next week and consider its future in the coalition.
"We have to value our strength, what we can do, on the other side, the impact of our decision, will our voters go along with us or will they reject us,... that is the scenario that we would like to discuss during our caucus."
The Conservative Alliance has six seats and the ruling SDL party has 28 in the 71 seat parliament.
Mr Vula says the SDL should remember that the Conservative Alliance holds the balance of power.