Forecasters say Tropical Cyclone Meena is intensifying rapidly east of American Samoa, with winds increasing to 110 kilometres an hour, within the next six to 12 hours.
The cyclone is moving east at about nine kilometres an hour, and is expected to travel slowly south east, towards the northern part of the southern Cook Islands group.
The Tropical Cyclone Centre in Nadi, Fiji, says a cyclone alert remains in force for the southern Cooks.
It warns of gales, scattered showers and isolated thunderstorms about Palmerston Atoll in the Cook Islands tonight.
It says heavy rain and squally thunderstorms will develop there tomorrow, with damaging heavy sea swells, and sea flooding likely over coastal areas tomorrow.
In American Samoa the weather service has been warning of high winds in Manu'a as the cyclone moves away.
Schools have been shut and all internal flights are grounded.