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By Renju Jose

SYDNEY, March 5 (Reuters) - Australia braced for a rare east coast tropical cyclone that is swirling towards Brisbane, its third-most populous city, with authorities urging residents in flood-prone suburbs to evacuate soon.

Storm warnings on Wednesday stretched for more than 500 kilometres (311 miles) across the coast in the states of Queensland and New South Wales, impacting millions of people.

Destructive wind gusts of up to 155 kph (96 mph) could develop from Thursday afternoon and tropical cyclone Alfred is expected to land as a category-two storm early on Friday morning near Brisbane, Queensland's capital.

Total rainfall from the event could be as much as 800 mm (31.5 inches) in some regions, more than the average total for March and could cause life-threatening flash flooding, the Bureau of Meteorology said.

"This is a very rare event for south-east Queensland ... it has been many decades since this part of the state experienced (a cyclone)," Queensland Premier David Crisafulli told reporters.

He called on residents to heed evacuation orders.

"If you are in a storm tide zone or you're in an area where you know there is riverine flooding, you really need to consider and think about your evacuation plan now," Crisafulli said.

Prime Minister Anthony Albanese said heavy-lift helicopters have been deployed and offered to "provide whatever resources are required" for the state governments.

Many residents have left their homes as authorities rush to open evacuation centres. Sandbags are in short supply and supermarket shelves have been stripped bare as people stock up on essentials.

Southeast Queensland and northern New South Wales were last hit by a cyclone more than half a century ago in 1974. The last time a cyclone threatened Brisbane was in 1990 but the system tracked south just before reaching the city.

Schools in southeast Queensland will close and public transport will shut down on Thursday and Friday.

A total of 122 schools in the north of New South Wales will be closed on Wednesday and Thursday, and vulnerable residents will be urged to relocate by Thursday morning, New South Wales Premier Chris Minns said.

"We need to bunker down over the next 48 hours and get through what may be a very difficult time," he told reporters.

Qantas QAN.AX said it had cancelled a number of flights from southeast Queensland and northern New South Wales and more were likely over the coming days.

The Ladies European Tour co-sanctioned WPGA Championship event was called off and the Australian Football League has postponed two matches in southern Queensland.

(Reporting by Renju Jose in Sydney; Editing by Stephen Coates and Edwina Gibbs)

((renju.jose@thomsonreuters.com;))