There's an active convergence zone slowly moving around the Cook Islands, with Palmerston to continue to experience winds up to 100 kilometres per hour.
A gale warning remains in place for Palmerston and a strong wind warning for the rest of the Cooks.
The cyclone is expected to continue in a southerly direction between Palmerston and Niue, which are located hundreds of kilometers to either side of the storm system.
It is forecast to retain its strength until Wednesday when it is expected to weaken and veer westwards.
On Sunday, or Saturday local Cook Islands time, a Palmerston resident, Will Rowe, said there were fallen fronds and coconuts and the lagoon was boiling like a cauldron.
The executive officer of the Palmerston Island Administration, Arthur Neale, said residents on the north of the island close to the shore had moved to homes further inland.