Prime Minister Frank Bainimarama's Fiji First has not conceded defeat, while a coalition of three parties say they have a combined majority and have agreed on People's Alliance leader Sitiveni Rabuka as prime minister.
In a statement on Facebook, Bainimarama said the military "has been deployed to complement the Police in maintaining law and order".
Bainimarama has been prime minister for 16 years, taking power in a coup, and later winning two democratic elections in 2014 and 2018.
New Zealand's Foreign Minister Nanaia Mahuta said New Zealand was "aware of the statement from Fiji's Police Commissioner".
The prime minister must be voted in by more than 50% of lawmakers on the parliament floor.