The Minister for Women's Safety has suggested an investigation into a "threatening" phone call to Grace Tame could be dropped if the 2021 Australian of the Year does not wish it to proceed.
On Wednesday Ms Tame used a National Press Club speech to allege someone from a "government-funded organisation" called her to warn her against criticising Mr Morrison in the lead-up to the 2022 Australian of the Year announcement.
The federal government has launched an investigation into the claim, led by Minister for Women's Safety Anne Ruston.
Liberal senator Jane Hume said the source of the call, which Ms Tame said was "threatening", remained a mystery.
She said the Australia Day Council had said the call did not come from within its ranks.
"We don't know whether it was a bloke or a woman," Senator Hume said.
"We just know, according to Ms Tame, it was someone from a government-funded entity.
Senator Hume said the Prime Minister's Office said the call to Ms Tame had not been ordered by Mr Morrison.
"Minister Ruston is going to make some inquiries about who would make such an allegation because it wasn't a directive from the Prime Minister," Senator Hume said.
Grace Tame says minister's investigation 'misses the point'
Ms Tame has not named the individual involved, and Senator Ruston said the government needed more information.
"I'd be keen to get to the bottom of what Ms Tame has said has happened because I think it's completely unacceptable that anybody would be seeking to pressure somebody to be silenced," Senator Ruston told ABC Radio Adelaide on Thursday morning.
"That just goes against everything I believe in.
"But Ms Tame has, subsequent to her comments, indicated on Twitter that she doesn't wish for it to be looked into further.
"But you know what … whoever did it should just front up and apologise and actually out themselves because it is an unacceptable thing to do."
Ms Tame wrote on Twitter that an investigation into the call was "the very same embedded structural silencing culture that drove the call in the first place and misses the point entirely".
"It's not about the person who made the call. It's the fact they felt like they had to do it," she said.
Senator Ruston said the Press Club address was the first time she had heard about the phone call.
"All I said yesterday was that we would be happy to look into the matter and we remain happy to look into the matter if that's what she would like us to do," the senator said.
"She subsequently tweeted … that wasn't the point of why she made the comments, and I absolutely respect that too."
Senator Ruston said the government was still invested in the next national plan to end violence against women and children, including sexual violence.
'Then I heard the words, 'with an election coming soon'
Ms Tame, who was named 2021 Australian of the Year for her advocacy for survivors of sexual assault, told the press club the caller was "asking for my word that I would not say anything damning about the Prime Minister on the evening of the next Australian of the Year awards".
"'You are an influential person. He will have a fear,' they said. What kind of fear, I asked myself?"
"And then I heard the words, 'with an election coming soon'.
A spokesperson for the Prime Minister said Mr Morrison and his office only became aware of the allegation during Ms Tame's speech.
"The Prime Minister has not and would not authorise such actions, and at all times has sought to treat Ms Tame with dignity and respect," the spokesperson said.
"The Prime Minister and the government consider the actions and statements of the individual as unacceptable."
The spokesperson also said the individual should apologise.
Later asked what she had said in response, Ms Tame said: "It doesn't matter now."
