The opposition has accused the Tánaiste of "hiding behind lame excuses" in his defence of sharing information about a GP contract deal with a rival doctor organisation.
Sinn Féin's health spokesman claimed Leo Varadkar's actions were "not just informal" but "inappropriate and wrong".
David Cullinane said he did not accept Mr Varadkar's explanation and that the Tánaiste "must come clean" and accept that he should not have handed over the documents.
The Tánaiste was accused on Saturday of leaking "confidential" documents of an agreement reached between the Department of Health, the HSE and the Irish Medical Organisation (IMO) to rival organisation the National Association of General Practitioners (NAGP).
Mr Varadkar has denied the allegations and branded them "inaccurate" and "grossly defamatory".
He acknowledged that he did pass information via an "informal communication channel" and admitted it was "not best practice", but he insisted there was nothing "unlawful" about his actions because the information was already in the public domain at that stage.
Mr Varakdar denied wrongdoing and said he had sought legal advice on the claims contained in an article in the current edition of Village magazine.
Mr Cullinane said: "I don't think that it is acceptable that the Tánaiste is hiding behind lame excuses.
"The facts for me here are clear that Leo, as the leader of Fine Gael and Taoiseach at the time, passed on a document to a friend about sensitive negotiations involving hundreds of millions of euro of taxpayers' money.
"It was clearly a document that was marked confidential."
Mr Cullinane told RTÉ's This Week: "He's hiding behind excuses here and he has to come clean and accept that this was absolutely and completely unacceptable and inappropriate. He talked about informal communications channels. It wasn't just informal. It was inappropriate. It was wrong."
He added that the Tanaiste "knows in his heart that this was wrong".
"People have to have faith that the Tanaiste can act in good faith when he's acting on behalf of the State and this does strike to the very heart of his credibility," he said.
The Finance Minister said it is "not common" practice for the Government to share confidential negotiation documents.
But Paschal Donohoe said the Tánaiste had only shared the Irish Medical Organisation (IMO) GP contract after negotiations had concluded and after the details had been broadly circulated.
Leo Varadkar confirmed on Saturday that he had provided a draft agreement between the Department of Health, the HSE and the IMO to rival organisation the National Association of General Practitioners but that he did so when the information was already in the public domain.
Mr Donohoe told RTÉ's This Week programme that the Tánaiste had acknowledged that the way the information was shared was "not best practice".
"He's also made it clear that he will go into the Dáil to answer questions in relation to this," he added.
"A key point that was guiding what he did, and our efforts to reach an agreement with GPs at that point, was firstly to try to improve the services available to patients through a new GP contract and secondly to get as many GPs as possible to enrol into the new contract."
Asked if it was common for Government to hand over confidential documents, Mr Donohoe said: "It's not common and that's why the Tánaiste said what he did yesterday.
"He said very clearly that it wasn't best practice, he acknowledged it could have been done differently.
"But it's very important to emphasise that when the information was shared it was after the negotiation had been concluded in relation to the agreement, it was after a press conference had been done on the agreement and it was after the Government had agreed on the new agreement and the details that we were referring to were being broadly circulated and broadly reported on."
He added that he had worked with the Fine Gael leader on "countless negotiations" and that at all times the Tánaiste had been "guided by trying to do the right thing".
Paschal Donohoe said the Taoiseach had spoken to Mr Varadkar about the matter on Saturday and that Micheál Martin had "outlined his concern in relation to the way the information had been shared".
The Finance Minister also said Mr Varadkar was "very aware" of the duties he has to the Dail to answer questions from opposition parties, and that any questions would "of course be answered".