Forecasters say Cyclone Percy is rapidly weakening as it continues to move over open water south east of Rarotonga.
The lead forecaster at the New Zealand met service, Oliver Druce, says the storm is still technically a cyclone, but will turn into a depression within the next six to twelve hours.
The cyclone wrought extensive damage to buildings and infrastructure in all three atolls of Tokelau, as well as in Pukupuka and Nassau in the northern Cooks.
Chief Inspector Teroi John Tini from the Emergency Operations Centre in Rarotonga says aid could reach those affected in the northern Cooks by tomorrow.
Meanwhile, forecasters in Fiji are keeping a watch on two tropical depressions.
The regional specialised meteorological centre in Fiji says there is one depression between Rotuma and Vanua Levu but its potential to develop into a cyclone in the next two days is low.
The centre at Nadi points out another system near the main islands of Fiji is not expected to turn into a tropical cyclone in the next one to two days.