At 0300 local time (1400 GMT) Cyclone Evan was to the north of Vanua Levu, tracking south-westwards.
Strong wind warnings are in force for the whole country and an alert for destructive seas has also been issued.
Evan is 480 kilometres wide and packing winds of 230 kilometres per hour, making it the strongest cyclone to threaten the country in 20 years.
Forecaster Terry Atalifo from Fiji's Meteorological Office, says the main island of Viti Levu will start feeling the worst effects of the category four system on Monday.
"There's a possibility that they could feel storm-force winds as this cyclone tracks south-westwards." he said.
Authorities are trying to evacuate tourists and residents in low-lying areas.
The international airport at Nadi is packed with people who have been evacuated from luxury resorts on outlying islands.
But Fijian officials say with most flights already booked or rescheduled, holidaymakers have little chance of getting out before the storm arrives.
Resort manager Gordon Leewar says his guests have decided to stay put and wait for the cyclone to pass.
"We have five couples on our property at the moment and they're really happy to stay, we've asked them whether they want to be evacuated but they've said 'no, we want to stay and we hope for the best'".
The Australian and New Zealand Governments say they are closely monitoring the movement of Cyclone Evan.
Both countries say that their concern is for the safety of its citizens in Fiji, as well as the welfare of all Fijians.
Canberra and Wellington say they are prepared to assist Fiji in all areas and remain on standby.
Emergency services in Fiji are preparing for the worst, while Fiji's Navy has urged sea farers not to travel out to sea during disasters.
Fijians living in low-lying areas have been urged to move to evacuation centres on higher ground.
Fiji's Meteorological Office expects the cyclone to intensify briefly as it moves across the country, before weakening as it leaves Fiji.
"Within the next 24 hours we will see some slight intensification but [after that] we expect the system to weaken as it moves further south into cooler waters." Mr Atalifo said.
On high alert
There are fears the category four cyclone could strengthen and generate winds of up to 300 kilometres an hour.
A gale warning has been issued for Cikobia, Taveuni, Vanua Levu and nearby smaller islands and northern Lau group.
A tropical cyclone alert remains in force for Viti Levu, Lomaiviti, Yasawa and Mamanuca group. A strong wind warning remains in force for rest of Fiji.
Cyclone Evan is forecast to bring heavy rain, thunderstorms and flooding of low-lying coastal areas.
People on the island of Vanua Levu, and the smaller island groups being urged to head to emergency and evacuation centres.
Fiji's interim Prime Minister Frank Bainimarama has met with officials in Suva to discuss all aspects of disaster management before and after the cyclone.
Mr Bainimarama has urged public servants in the northern and western division to remain at home and wait further instructions.
"Because this is the festive season, I ask you to consider cancelling social events and to act responsibly, all of us need a clear mind for what is bearing down on us.
"Only those working in essential services should be at work and they should liaise closely with their departments on this."
Mr Bainimarama says the goverment is coordinating the provision of emergency supplies, including food and water to areas that are likely to be affected.
Today's briefing also saw the Fijian prime minister repeat his earlier address to the nation, stressing the severity of the storm and the threat it posed to the country of 900,000 people.
"It has winds up to 180 kilometres an hour which may intensify, and if the weather forecasters are correct it will affect Fiji in a very damaging way, bringing about destructive winds and flooding," he said.
"I cannot stress how serious this is, every Fijian will be affected."
Fiji's Permanent Secretary for Information, Sharon Smith-Johns, says many people have heeded the message and fled to higher ground.
"There are people that have already taken precautions. They know that they live in flood prone areas and they're moving to higher ground or moving in with relatives, so there is quite a lot of movement around Suva...and in the rural areas."
More than 20 evacuation centres have been set up in northern areas of Fiji, with centres also set up in the country's western division.
"We are advising people to move to high ground, those who are living in lower-lying areas," Asesela Biuviti of the national disaster management office said.
People on the island of Vanua Levu, and the smaller island groups are already heading to emergency centres
The government says troops in all parts of the country are ready to help with recovery assistance and search and rescue operations.
Ms Sharon Smith-Johns says the government feared Evan could be as devastating as Cyclone Kina which killed 23 people and left thousands homeless in 1993.
"This is going to be an extremely bad cyclone to hit us and probably the worse that we've seen since Cyclone Kina.
"It will be quite destructive. We've seen what's happened in Samoa and all we can do is be prepared here lucky we've had a week's notice of this," she said.
"All the agencies have been deployed, emergency services on standby, evacuation centres are open, rations have gone out.
"Now it's just a matter of continuing to clean up our own backyards and putting cyclone shutters up and waiting."
Ms Smith-Johns has reiterated government's call for the public to refrain from unnecessary travel.
"Put your safety and your families' safety first and keep listening to the radio before attempting to move around."
The cyclone appears to have bypassed northern Tonga, where it was expected to bring gale force winds and heavy rain to the country's northern islands.
Destruction in Samoa
Fiji's Prime Minister Frank Bainimarama has sent a message of sympathy to his Samoan counterpart, Tuilaepa Sailele.
The confirmed death toll in Samoa from the cyclone has risen to four, with another eight people missing and feared dead after being swept away when Apia's main river burst its banks.
"We send our special prayers and condolences to those who have lost loved ones in the disaster," said Mr Bainimarama.
"Every Fijian has been shocked and saddened by the destruction caused by the cyclone to the homes and lives of ordinary people and Samoa's infrastructure."
Mr Bainimarama says Fiji is on standby for any assistance.