A spokesperson for Bougainville during the civil war, Martin Miriori, says MPs must not push for the postponement of next year's election.
There have been discussions about delaying the poll for the Autonomous Bougainville Government because it may clash with consultations over the referendum vote.
Regular voting for the referendum was on Tuesday with counting to start on Saturday, after which consultations are to be held.
Mr Miriori, who had also led the Bougainville interim government and was a leader in the Bougainville Revolutionary Army, said he doubted the people would accept a delay.
A petition was being drafted by South Bougainville community governments, he said, which would ask the Bougainville Parliament not to entertain the idea of postponing the election.