"However island groups in southern Lau should take precautions against damaging gale force winds and heavy southerly swells as the TC moves closer in the next 24 hours", Na Draki said.
The Metservice said it expects Cyclone Gita to peak at a Category 4 event, but other regional meteorological agencies said the storm would reach Category 5, the most destructive wind-speed ranking.
A state of disaster has been declared in Samoa after a devastating cyclone ripped through the island.
The storm is forecast to be closest to the main island of Tongatapu at around midnight.
A massive clean up is under way across Samoa and American Samoa after they bore the brunt of the cyclone at the weekend. Tongatapu would be "pretty much exposed to the full brunt of the cyclone".
While Gita was upgraded to category three as it threatened Niue late last night, a sudden change of direction, lifted the threat and there have been no reports of significant damage.
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The storm is packing winds of over 160km/h and is forecast to intensify.
Mr Fa'anunu said because Tongatapu was low-lying, especially on the northern shores, associated storm surges also have people concerned.
Acting Prime Minister Semisi Sika issued a nationwide alert, saying he was "satisfied that an emergency is happening or is about to happen".
The Red Cross said residents were racing to identify strong buildings to be used for evacuations and to clean up debris such as loose wood or metal that could turn into unsafe missiles in powerful winds.
Hanna Butler, a spokeswoman for Fiji-based Red Cross Pacific, told Reuters that approximately 300 people had evacuated the Samoan capital, Apia, to escape flooding but were now returning to their homes.
Truckloads of troops were helping people batten down as the capital prepared for the cyclone and evacuation centres were opened across the kingdom.