A former prime minister of Fiji, Mahendra Chaudhry, says the regime's draft constitution should be to put to a referendum.
The regime is in the middle of a month-long exercise explaining its draft at sessions around the country and collecting people's feedback.
It says it has been pleased with the positive response.
But Mr Chaudhry says the best test of whether the regime document is popular is to put it to a vote.
"We challenge them to put it to a referendum, supervised by the international community and if the people accept it, we settle the dispute, if they don't, they should back off."
Mr Chaudhry is part of an opposition group which is circulating a petition to bring back the earlier draft dumped by the regime.
Fiji's Attorney-General Aiyaz Sayed-Khaiyum has dismissed the idea of a referendum saying there are constraints on time as well as practical and technical issues to consider.