Bougainville officials say almost all electorates have now completed voting in the elections, which are scheduled to run until next Monday.
Reports from returning officers in the autonomous Papua New Guinea region say polling has been completed in 31 of the 33 constituencies.
Another constituency, Eivo-Torau, in Central Bougainville, was expected to have finished by last night but because of issues with mobile phone reception, officials could not confirm.
The only place where polling is yet to be conducted is Tasman Island in the Atolls constituency of North Bougainville.
Voting there has been held up by bad weather which had prevented the polling officials from travelling there until yesterday.
The acting electoral commissioner, George Manu, has praised the tireless efforts of the polling officials, saying without their dedication, the staging of the poll would not have been possible.