The Tánaiste has denied that he acted unlawfully by sharing an agreement reached with the Irish Medical Organisation to a rival group.
The Green Party - Fine Gael and Fianna Fáil's third coalition partner - has called on the Tánaiste to give a "full and detailed account" to the Dáil, and allow time for questioning afterward.
A spokesperson for Mr Varadkar had earlier said he would make a statement and take questions in the Dáil next week on the issue.
In a statement he described an article published in the Village magazine about him as "inaccurate and grossly defamatory". The Fine Gael leader said he has sought legal advice on the content of the article.
The article alleges that Mr Varadkar passed on a "confidential" agreement agreed with the Irish Medical Organisation to Dr Maitiú Ó Tuathail, the head of a rival organisation, the National Association of General Practitioners.
Mr Varadkar admitted providing an agreement reached with the IMO through what he termed an informal communication channel to a rival group was not best practice.
He said that on Friday, 5 April 2019, the agreement was publicly announced by the IMO.
Mr Varadkar said the fact that an agreement had been reached, and the nature of that agreement, was not something that was confidential or sensitive after 6 April.
The statement says the then taoiseach did provide a copy of the agreement to Dr Ó Tuathail on a date between 11 and 16 April, 2019.
It says the agreement was provided to Dr Ó Tuathail, as President of the NAGP, in circumstances where the taoiseach believed the deal was a positive one for GPs.
It said Mr Varadkar hoped to use Dr Ó Tuathail's influence to encourage all GPs to accept it, including those represented by NAGP.
The statement said that given it had been extensively negotiated between Government and the IMO, many people outside Government in the IMO were already well aware of its content.
It says that Mr Varadkar accepts that the provision of the agreement by an informal communication channel to the president of the NAGP was not best practice.
It said he regrets that he did not ensure that it was provided in a more appropriately formal manner.
The statement says there was nothing in any way unlawful about the provision of the agreement to Dr Ó Tuathail.
The Taoiseach and Mr Varadkar have already spoken about the matter.
The Green Party said it noted the statement from the Tánaiste following the revelations in Village.
The party is calling on Mr Varadkar to give a full and detailed account to the Dáil on the issue, and to allow sufficient time for the statement followed by questioning.
"It is clear from what has been revealed that the passing on of sensitive information in this manner was not appropriate.
"The timelines and the full impact of the disclosure on all involved needs further scrutiny," the party said.
Michael Smith, editor of Village magazine, has responded to Mr Varadkar's statement.
Mr Smith said the NAGP considered that the document was confidential and messages published in Village confirmed this was the view of the NAGP.
Mr Smith added that Fianna Fáil TD Stephen Donnelly, who was an Opposition health spokesman at the time of the agreement was negotiated, told the Dáil on 16 April 2019 that he had been "denied" access to the "detail" of the agreement.
Socialist TD Paul Murphy has said Mr Varadkar's statement confirms that he gave Dr Ó Tuathail a copy of the draft agreement.
Mr Murphy asked whether Mr Varadkar will answer questions on the matter in the Dáil on Tuesday.
A number of Opposition TDs had called on the Tánaiste to address the matter following the publication of the article.
Earlier Sinn Féin spokesperson on Enterprise and Trade, Louise O'Reilly said: "Mr Varadkar has serious questions to answer."
The co-leader of the Social Democrats, Róisín Shortall, said the Tánaiste must make an immediate statement on the matter.
She said: "Social Democrats view with extreme concern allegations made in the current edition of the Village Magazine."
Additional reporting Mícheál Lehane