The United Front For a Democratic Fiji says there is genuine concern that elections promised for next year won't be held.
The group, which represents many of those who were removed from office in the 2006 military coup, says the regime is delaying the electoral process by delaying the constitution.
A member of the group, the National Federation Party's Raman Singh, says the date for the constitution's release has been put back constantly by the regime.
"The main reason for that doubt is the fact that the date for the promulgation of the constitution has been extended from June to July and now we believe it's in September so we feel that does not give enough time to do all the other preliminary work to have the election. That's where the doubt rises from."
Raman Singh says he cannot say whether he believes the constitution is being deliberately withheld.
The statement says the regime leaders, Commodore Frank Bainimarama and Aiyaz Sayed-Khaiyum, have sensed that the regime has very little, if any, support.