The Cook Islands Meteorological service says tropical cyclone Tuni has been downgraded to a tropical depression.
An observer at the Cook Islands Met Service, Manea Maratapu, says people are still being advised to take care as a strong wind warning remains in place.
He says the tropical depression is expected to have passed through the Cook Islands within the next 36 hours, but people are still being asked to stay alert.
"We'll be expecting some heavy rain, thunderstorm, and also some strong winds will be affecting the Southern Cooks."
Mr Maratapu says while there have been bursts of heavy rain, there have so far been no reports of flooding.