The opposition is demanding the head of Julia Gillard amid new revelations about the prime minister's involvement in the AWU slush fund scandal.
Senior Liberal Christopher Pyne says Ms Gillard's position is "entirely untenable".
"If the prime minister had any respect for the parliament and the Australian public or the Labor caucus she would resign as prime minister today," Mr Pyne told reporters in Canberra on Thursday.
He was responding to reports that Ms Gillard admitted during a secret internal inquiry to writing to a West Australian government department to help overcome its objections to the creation of an association for her then boyfriend and client, union official Bruce Wilson.
The revelation, contained in a document released on Thursday after 17 years, comes after days of stonewalling by the prime minister, including in parliament, on the question of whether she had personally vouched for the Australian Workers' Union Workplace Reform Association.
Ms Gillard has avoided answering repeated questioning from Deputy Opposition Leader Julie Bishop on whether she wrote to the WA Commissioner for Corporate Affairs in 1992 to vouch for the bona fides of the association.
Mr Pyne said Ms Gillard had insisted she only had "a passing involvement" in the association.
"I'm not Hercule Poirot, but I can work out what's going on here," he said.
Earlier, Opposition Leader Tony Abbott said it appeared Ms Gillard gave false information to the WA authorities.
"For a senior lawyer to make false claims to an important statutory body like this is a very, very serious matter ... it's in breach of the law I would think and it's certainly very, very unethical," he told the Nine Network.
Mr Abbott later told reporters in Canberra: "If the prime minister has an explanation, she better give it, she better give it quick smart".
Parliamentary secretary Richard Marles said the opposition had "an utter obsession" with what Ms Gillard was doing 17 years ago.
"Let's take a deep breath about these so-called revelations coming out today," he told reporters.
"That is what a lawyer would do under instructions from their client."
It was not remarkable Ms Gillard could not recall a letter she wrote nearly two decades ago, Mr Marles said.
"They (the opposition) think they've got a smoking bazooka going on here.
"But when they pull the trigger, what they've got is a popgun."
Asked whether Ms Gillard's position was now untenable, Liberal senator Simon Birmingham said the prime minister had always lacked authority.
"She came to the prime ministership lying about her intentions for the job," Senator Birmingham told reporters in Canberra.
"She lied to the Australian people at the last election," he added, referring to her promise during the 2010 election campaign not to introduce a carbon tax.
"What the latest revelations indicate is that Julia Gillard may well have been just as adept at lying way back in her professional career in 1992 as she was to Australian voters in 2010."
Cabinet minister Bill Shorten dismissed the latest revelations, saying Ms Gillard gave advice on the incorporation of an association.
"That's it," he told Sky News.
"As far as I can tell any piece of correspondence is part of the process of setting up the fund."
Mr Shorten, a member of the AWU, insisted there was no smoking gun.
"There's ... so much smoke and fiddle and faddle from the opposition," he said.
