A Virgin Australia jet was cleared to take off last Sunday but swiftly forced to cancel, as a Qantas plane already had permission to cross the runway 1.3km away at Sydney Airport.
The incident was not reported for four days, the Australian Transport Safety Bureau (ATSB) said, as Airservices Australia contended it did not meet notification thresholds.
News of a third incident comes after the high-profile near-miss earlier last Sunday when a Jetstar pilot was forced to break to avoid a Qatar Airways plane as the Middle Eastern jet was towed across the tarmac, giving a flight attendant minor injuries.
That came after an episode on July 27 when two Qantas planes were cleared to approach a runway at the same time.
On Friday, ATSB chief Angus Mitchell confirmed his body was investigating the Virgin Australia-Qantas incident from last Sunday.
''It's really important we have a thorough understanding of what occurred, the environment it occurred in, so any recommendations we make are actually going to lead to improvements,'' he told reporters in Canberra.
Airservices Australia reported the incident on Thursday and Mr Mitchell said he was ''still trying to understand'' the hold-up.
He noted training underway in the air traffic control tower may have affected procedures.
"It is an incident, regardless. We do know we had two laden aircraft both given clearance on the same runway, that reaches the threshold for an incident for us," he said.
Airservices Australia Rob Sharp disagreed when he spoke to reporters later on Friday.
''Firstly, controllers immediately rescinded the clearance, they recognised there was a Qantas aircraft 1.3km away approaching the runway," he said.
"Secondly, the aircraft remained stationary; and thirdly the distance of 1.3km is quite substantial … however we're quite open to reviewing the data that surrounds it."
Prime Minister Anthony Albanese said there had to be immediate reporting of any incident.
''We have an extraordinarily safe record here in Australia … we'll continue to make sure that we are very vigilant,'' he said.
NSW Premier Chris Minns said safety had to take precedent at the capital's airport.
"As regrettable as it is, flights are going to have to be cancelled if safety is compromised at all,'' he said.
"The main thing is we've just got to get those air traffic controllers trained up and deployed as quickly as possible.''
Civil Air president Scott Nugent previously told AAP Sydney Airport's control tower staff were stretched thin.
"They're just not putting enough in ... we can't just put people in and expect them to be working the next day,'' Mr Nugent said.
Mr Sharp previously said the organisation was recruiting more than it ever had been, but was competing for resources.
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