The 2021 Australian of the Year has spoken about receiving a call from "a senior member of a government-funded organisation" on August 17 about the 2022 awards scheduled for January.
Ms Tame told the National Press Club on Wednesday the person asked "for my word that I wouldn't say anything damning about the prime minister on the evening of the next Australian of the Year Awards".
"You're an influential person. He'll have a fear ... with an election coming soon'," she recounted the person saying.
Women's Safety Minister Anne Ruston labelled it "a completely unacceptable" thing for a publicly funded organisation to do and confirmed the government was investigating.
The prime minister's office said Mr Morrison "has not and would not authorise such actions and at all times has sought to treat Ms Tame with dignity and respect".
It called on the individual, who Ms Tame declined to name, to apologise.
"Those comments were not made on behalf of the PM or PMO or with their knowledge," the statement said.
"The PM and the government consider the actions and statements of the individual as unacceptable."
The National Australia Day Council, which coordinates the awards, said it had contacted Ms Tame for further information.
It also canvassed various personnel who spoke with Ms Tame over the past year, "none of whom had interactions ... that would be considered 'threatening' as the 17 August conversation has been described".
"The Australian of the Year Award is just that – an award, not a role," the organisation said.
"Award recipients are free to use the platform the award provides any way they see fit, with the support of the NADC."
Ms Tame panned the government's investigation and called on the prime minister to "stop deflecting".
"It's not about the person who made the call. It's the fact they felt like they had to do it," she tweeted.
She earlier drew comparisons between the call and the child sexual abuse she endured at the hands of a teacher.
"I remember standing in the shadow of a trusted authority figure being threatened in just the same veiled way," Ms Tame said.
"I would rather go down as a disappointment to an institution than sell out as a pandering political puppet to the corrupt forces that coercively control it."
Ms Tame, addressing the National Press Club alongside former Liberal staffer Brittany Higgins, dismissed Mr Morrison's apology delivered a day earlier for assault and harassment on Capital Hill.
An acknowledgement of harm caused was among 28 recommendations from Sex Discrimination Commissioner Kate Jenkins. Her review found one third of Commonwealth parliamentary workers surveyed had been sexually harassed.
Other recommendations from the commissioner were introduced in the Senate on Wednesday.
Ms Higgins, whose allegation about being raped in the office of then-defence industry minister Linda Reynolds in 2019 triggered various reviews, indicated she didn't think much of the government's assurances.
"I don't care if the government has improved the way that they talk about these issues. I'm not interested in words any more. I want to see action," she said.
Ms Higgins called out Mr Morrison's propensity for "shocking" and "offensive" language about issues of women and their safety.
"What bothered me most about the whole 'imagine if it were our daughters' spiel wasn't that he necessarily needed his wife's advice to help contextualise my rape in a way that mattered to him personally," she said.
"I didn't want his sympathy as a father; I wanted him to use his power as prime minister."
Ms Higgins was among women invited to Tuesday's apology in the House of Representatives at the last minute after the government was lashed for leaving her out.
"It was deeply emotional in a way that I wasn't anticipating," she said of the apology.
"I'm so grateful that I had the opportunity to be there because it made it so much more tangible."
