Forecasters in Fiji say Tropical Cyclone Meena is now east of American Samoa, heading east at a speed of five knots.
All public schools in the territory have been closed and authorities have advised the territory's residents to begin preparations to protect their families and homes.
The Fiji met service says the cyclone is intensifying rapidly and is expected to curve south east towards the southern Cooks later today.
Forecasters warn of damaging gale-force winds over Palmerston Island and other northern parts of the southern Cook Islands in the next 36 to 48 hours.
Chief Inspector Teroi John Tini of the Cook Islands police is working at the emergency operations centre in Rarotonga.
"We are alerting our people that there is a tropical cyclone near the area and to take precautionary measures, to listen to the radio and not to be complacent."
Chief Inspector Tini says the emergency operations centre has been set up as a temporary measure whilst any threat exists.
He's receiving hourly reports from centres in the outer islands.