A tropical cyclone was racing towards Australia's remote Norfolk Island on Saturday, with forecasters warning its 2,000 residents to prepare for "destructive winds" and a deluge of rain.

Tropical Cyclone Gabrielle is then expected to hit northern New Zealand, where a huge clean-up operation is still underway after devastating floods at the end of January.

Australia's weather bureau said the storm could whip up gusts of up to 155 kilometres per hour (96 miles per hour) as it approached Norfolk Island, which lies about 1,500 km (930 miles) northeast of Sydney.

Norfolk Island administrator Eric Hutchinson said the worst of the cyclone was expected Saturday evening, but strong winds had already caused some power outages.

"We are expecting power outages, trees coming down, the potential for houses to lose roofs," he told national broadcaster ABC.

The cyclone was downgraded to Category Two on Saturday morning, but Hutchinson said it remained a potentially dangerous situation.

"We've had a couple of days to prepare, so we'll deal with the recovery as needed," he said.

Australia's weather bureau said the storm would bring "destructive winds, heavy rainfall, abnormally high tides and damaging surf" to Norfolk Island, which has suspended flights until it passes.

The cyclone will then approach New Zealand on Sunday evening, according to the country's MetService, bringing "significant heavy rain" to the North Island.

Emergency shelters are already being set up across Auckland, a city of 1.6 million people that is still under a state of emergency following heavy flooding two weeks ago.

Now known as an idyllic tourist destination, Norfolk Island was once a notoriously brutal British penal colony dubbed the "Hell of the Pacific".

It was abandoned by the mid-1850s but later re-settled by descendants of the British sailors who carried out the infamous mutiny on the HMS Bounty in 1789.