Cyclone Ella, which has formed south of Samoa, is forecast to intensify to Category 2 as it moves towards Fiji.
The Category 1 cyclone is forecast to move towards Fiji at about 7km/h.
It is expected to move west, past Tonga's northernmost islands.
The new storm in the Pacific comes as Cyclone Donna, now Category 3, arrives in New Caledonia, with wind gusts up to 230km/h.
The Fiji Met Service said Ella was intensifying and was forecast to be Category 2 by Thursday.
It was expected to make landfall on Vanua Levu in Fiji late on Thursday evening or early Friday morning.
Samoa's weather office has issued a heavy rain warning for the whole country with possible flooding in vulnerable areas.
The warning has come with advice from the Disaster Management Office for members of the public living near river banks and low-lying areas to be on alert.
The office said landslides were possible and people living on land that could be affected should consider moving to safer areas.
Disaster authorities in Vanuatu, meanwhile, which was lashed by Cyclone Donna earlier this week, were continuing to assess damage to houses and crops in the country's north.