The Fijian Political Party, the SVT, has called on the Great Council of Chiefs not to bow to political pressure but to stay neutral when it considers the nomination of a vice president.
The Fiji Sun quotes the SVT spokesperson, Ema Druavesi, as saying the Great Council should not prejudge President Ratu Josefa Iloilo's recommendation but instead look at the merits of his choice.
Ms Druavesi says this is more so as the Great Council of Chiefs comes under the ministry of Fijian affairs which is the prime minister's portfolio.
She says politically biased decisions could divide the Fijian people.
The SVT's comments follow a threat by some pro-coup chiefs to oppose President Iloilo's nomination if they believe it has been influenced by the military.
The chiefs, who do not want to be named, say this will amount to a vote of no confidence in President Iloilo and force him to resign.
Fiji's military has warned these chiefs not to intimidate President Iloilo in his nomination of a vice president, adding that the army will stand by its commander-in-chief.