Russia-born Parnov worked at the Western Australian Institute of Sport (WAIS) between 1998 and 2019, when he quit after an investigation into claims of inappropriate behaviour was launched.
Parnov has never been tried or convicted over the allegations and attempts by AFP to reach him via social media were not immediately successful.
He coached some of Australia's greatest Olympic champions, including Paris gold medal-winning pole vaulter Nina Kennedy and Steve Hooker, who won the title at Beijing in 2008.
An investigation by The Australian newspaper alleged he preyed on a succession of vulnerable young women, many of whom complained but were reportedly told he was too important to the sport's success to be sacked.
It cited "a trove of texts, emails and incriminating video, as well as secret reports of incidents that should have been reported to police".
The newspaper said Parnov was believed to now be in Russia and did not respond to its questions.
The newspaper claimed his behaviour was ignored and then kept secret by WAIS, which declined to give details of its investigation when Parnov stood down in 2019.
Athletics Australia said it noted "the highly concerning reports" about his conduct and WAIS' responses to complaints.
"The reports identify patterns of behaviour that are totally unacceptable and deeply distressing, and we are profoundly sorry for the harm that they caused to athletes and staff," chief executive Simon Hollingsworth said in a statement.
"We support those who have spoken up and encourage any others who may have experienced unacceptable behaviours to come forward and speak to us confidentially so that further action can be taken."
Hollingsworth said that when informed by WAIS of its findings from the 2019 probe, it revoked Parnov's coaching accreditation and imposed a lifetime ban.
It has now asked Sport Integrity Australia, a government agency, to support a review into how Athletics Australia acted while Parnov was coaching, including how complaints were managed.
'Duty of care'
WAIS said in a statement it was "appalled" by Parnov's alleged behaviour.
"WAIS had a duty of care to athletes and it is clear that in the case of Parnov, the organisation did not do enough to protect them," it said.
"The WAIS board is profoundly sorry for the hurt and trauma experienced by these athletes and recognises their courage in speaking publicly about terrible events that should never have occurred."
The organisation admitted to being aware of some claims against Parnov, but the scale of allegations reported by the newspaper was "far more extensive than previously known".
It added that when a new board was appointed in 2023, it commissioned an independent analytical review of Parnov and WAIS' actions and had encouraged further investigation, including by the police, who confirmed they had been alerted to "potential criminal conduct".
Kennedy said athletes deserved to feel safe and supported.
"I believe the organisations responsible for safeguarding us failed to protect myself and others and enabled my former coach's harmful conduct to persist for over a decade," she told The Australian.
"This story has weighed on my shoulders for many years."
