'Akilisi Pohiva, whose reign was shortened by the August dissolution of parliament by the king, is up against his former deputy, Siaosi Sovaleni.
Mr Pohiva's democratic party won 14 seats in the subsequent November election giving him a slight majority in the 26 seat House.
So far there is no indication of any member of his party crossing the floor to support Mr Sovaleni, who was the third highest polling candidate in the election, although speeches are continuing and voting will be done in secret.
Once the prime minister is elected the process will continue for a speaker and deputy speaker of the house.
The prime minister designate will still need to be officially appointed by the King before he names his cabinet.
Photo: RNZ / Koro Vaka'uta 'Akilisi Pohiva