Voreqe Frank Bainimarama is Fiji's elected prime minister and his Fiji First Party will form the new government.

Supervisor of Elections, Mohammed Saneem, said he was confident that the final results would be announced by Sunday.

The election was the first for Fiji since a military coup led by Mr Bainimarama in 2006.

Provisional results, and projections based on a 80 per cent voter turnout, showed the party had secured more than 50 per cent of valid votes.

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The party would have achieved absolute majority and even if the main opposition party Sodelpa gets all the remaining votes, it would not be able to surpass Fiji First.

Five losing parties, including Sodelpa, have alleged fraud and said they would not be accepting the results.

Sodelpa leader Ro Teimumu Kepa said they were not doing this because they cannot accept defeat, but wanted the election commission to investigate.

Mr Bainimarama said the opposition objections did not come unexpected.

"This was expected from the losers," he said.

"They should just accept the result."

Fiji First general secretary Aiyaz Sayed-Khaiyum asked why these parties had not raised their concerns on polling day.

Besides Fiji First and Sodelpa, just the National Federation Party had more than 5 per cent of the votes to get parliamentary seats based on the provisional results.

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Fiji Women's Rights executive director Virsila Buadromo said there was expected to be nine women Members of Parliament.

This was 7 per cent more than the number of women voted in at the 2006 elections and the largest number of women representatives in Fiji's history.

More than 16 per cent of votes also went to female candidates, with the highest number going to Ro Teimumu Kepa.

The Multinational Observer Group acknowledged on Thursday that the elections did have some problems, despite saying it found the election to be credible.

"The MOG did, however, observe some problems, particularly in voter registration, pre-polling and postal voting, which stemmed at least in part from the short preparation time," the group said.

"These and other matters will be the subject of more detailed comment when the final MOG report is completed in due course."