Forecasters in Fiji say the centre of Cyclone Daman is not expected to make landfall on the country's second largest island, Vanua Levu.
The storm is about 50 kilometres north of Vanua Levu, and is expected to swing around to the South-East into water between Fiji and Tonga.
The hurricane warning remained in place overnight for north eastern parts of Vanua Levu, and the island of Cikobia.
Fiji's Meteorological Service says storm and gale warnings are in place for other areas, and has warned of possible flooding in low-lying areas.
The owner of a resort at Labasa on Vanua Levu has told the Fiji Times newspaper there's been heavy rain there, and winds of about 40 kilometres an hour.