Fianna Fáil communications spokesman Timmy Dooley said the public admission is necessary, despite saying his party is not demanding “a public execution” and is unlikely to table a no-confidence motion in Mr Naughten.
Mr Naughten was embroiled in controversy last week when it emerged he spoke informally with Heneghan PR official and former government press secretary Eoghan Ó Neachtain about the proposed INM takeover of Celtic Media.
The conversation was confirmed in leaked court records which showed Mr Naughten and Mr Ó Neachtain spoke about the deal on November 11, 2016, at which point Mr Naughten said he expected the deal to be referred to a Broadcasting Authority of Ireland inquiry.
The following day, then INM chairperson Leslie Buckley forwarded businessman Denis O’Brien an email from Heneghan PR executive Nigel Heneghan outlining the November 11 conversation.
However, during a Dáil debate on December 6, 2016, Mr Naughten said no decision had taken place on the deal and that the matter was still being discussed privately.
In a special Dáil debate last Wednesday, Mr Naughten insisted he had done nothing wrong, a position that was repeated by Taoiseach Leo Varadkar and other ministers.
Mr Dooley said the communications minister must this week provide a public statement accepting he acted wrongly, and if he fails to do so he must remove himself from any involvement in future media mergers.
“There needs to be an acceptance from Mr Naughten what he did was wrong. I’m not saying he did what he did with any intent, but the phone call is a fact.
“He can couch it in whatever way he wants, but if he can’t do that he should recuse himself from merger discussions.
“This doesn’t have to be fatal for him, we’re not looking for a public execution, but there is a need for the public to see a minister who has done this held to account,” said Mr Dooley.
On Sunday, the National Union of Journalists also called on Mr Naughten to “recuse” himself from media merger discussions due to last week’s revelations, a move also sought by the Social Democrats.