Niuatoputapu, in the north of Tonga, recorded winds gusts of up to 90 kilometres per hour yesterday.
Tonga Met Service forecaster Laitia Fifita said rainfall in the last 24 hours had exceeded 100mm and a heavy rain warning remained in force.
He said there should be a clearer picture later today of any damage caused by Tuni in the northern group.
The cyclone is forecast to pass close to Niue tomorrow.
The Fiji Met Service says while Tuni was only a category 1 storm, it has quite a sting due to the heavy rain bands associated with it.
Forecaster Misaeli Funaki said a strong wind warning had been issued for Niue but that would be reviewed later today.