US forecasters in Hawaii say Cyclone Meena in the northern Cook Islands will continue to intensify as it moves slowly south-east over the next 24 hours.
The Joint Typhoon Warning Centre says the winds around the centre of Meena will increase to a sustained 150 kilometres an hour within 12 hours, increasing to a sustained 160 kilometres an hour within 24 hours.
The latest warning says within 24 hours, the winds around the centre may reach up to 200 kilometres an hour.
Satellite pictures show a vast whorl of cloud lying between Suwarrow and Palmerston Atoll.
The Joint Typhoon Warning Centre says the storm's associated sea-surge effect will produce a maximum significant wave height of eight metres.
The centre predicts the storm will veer south east, heading directly towards Rarotonga.
Deputy Police Commissioner Maara Tetava says the emergency operations centre in Rarotonga has acted in response to concerns about small boats.
"We now have a register of all the boats in the outer islands, and we know exactly how many boats there are on each island, and we have a record of owners' descriptions and everything."
Deputy Commissioner Tetava warns no-one should now put to sea.
Police are also concerned Cyclone Meena may swamp the low-lying atoll of Palmerston.
Jason Brown reports from Rarotonga.
Palmerston is one of the most remote atolls in the Cook Islands, with less than 60 people. It is also one of the most low-lying, with police on Rarotonga holding concerns for their safety.
This morning the cyclone was still more than 300 kilometres north-west of Palmerston, but is expected to pass within 100 kilometres within the next 24 hours. Cook Islands police hope that Palmerston may be protected from most storm surge by its reef and large lagoon.