Virgin Australia Flight 740 from Gold Coast to Melbourne on October 27 received instructions from the prankster as it approached the runway at Melbourne's main airport at Tullamarine, with flight data showing it then climbed to 3,800 feet and circled over the state capital, The Age newspaper reported.
The unknown caller later that day called air traffic control and pretended to be a light aircraft pilot with engine trouble, the Australian Broadcasting Corporation reported.
"As a result of the unlawful interference with air traffic control broadcasts over several weeks, the AFP (Australian Federal Police) has today issued a call for public help for any information that will result in the identification and arrest of the person responsible."
Virgin Australia was not immediately available for comment, but its pilots' association warned of the potential dangers.
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"Unauthorised radio transmissions is a very rare event," John Lyons, the president of Virgin Independent Pilots Association, which represents Virgin pilots in Australia and New Zealand, said today.
Lyons said the alleged manoeuvre in which the aircraft was asked to "go around", where a landing approach is aborted, was not dangerous in itself.
"It's where (the plane) goes after that," he said.
"He (the pilot) could go around and it may well be that there is another aircraft which has just been cleared to take off on another runway, in which case you could go into an unprotected area and you could get two aircraft in close proximity to one another, and that would be a dangerous situation."
"The airlines have been briefed to ensure the advice has been passed on to their pilots and to ensure appropriate measures are in place."
Airservices Australia said safety was not affected by the hoax calls.
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