Minister for Communications Patrick O'Donovan is no longer seeking a review of media coverage of fuel protests despite his comments yesterday.
It comes after the minister met with Coimisiún na Meán officials today.
It is understood that the minister and the media regulator engaged constructively with each other regarding their respective responsibilities and independence of function.
A spokesperson for the regulator said: "An Coimisiún confirmed to the minister (and) said that it would follow up on statutory complaints regarding coverage of the fuel protests, as set out in legislation."
They said the regulator has received a "number of contacts from members of the public relating to broadcast coverage of recent fuel protests.
"In the first instance, we advise members of the public who wish to complain about broadcast content to complain to the broadcaster concerned. If they are unsatisfied with the response they receive from the broadcaster, they can contact Coimisiún na Meán.
"All complaints received by An Coimisiún will be processed, as standard under our statutory complaints handling process," they added.
No need for any sort of 'formal review' - Harris
Earlier, Tánaiste Simon Harris said that there is no need for any sort of "formal review" into media coverage of the recent fuel protests.
He was speaking after Mr O'Donovan said that he would be asking Coimisiún na Meán to review media coverage, including coverage from RTÉ News, of the protests.
Mr O'Donovan said he would be asking if the coverage was "balanced or was it skewed and I think that's a role for Coimisiún na Meán".
"Coimisiún na Meán may turn around to me and say 'nothing to see here, move along move along', but I'm going to ask them the question anyway," he said.
However, when asked about these comments on his way into a Cabinet meeting, Mr Harris said he is "a big supporter of freedom of the media, freedom of the press, as is the Government, as is the minister".
He said Mr O'Donovan "will be bringing forward legislative change later this year to further underpin the importance of freedom of the media".
"In line with a number of European developments, free media, a robust media, is an absolute, vital part of our democracy," he added.
"Of course, at the end of any difficult period, you can look back and say, at a moment a national crisis, can we get information out there? Are there learnings? But I certainly don't think there's any need for any sort of formal review. These are matters for Coimisiún na Meán."
The Tánaiste said the media "like everybody in the country, were doing their best to deal with a fast evolving, very difficult situation" during the protests.
Yesterday, the National Union of Journalists described the remarks by Minister O'Donovan as "sinister and deeply disturbing".
The union's assistant general secretary, Séamus Dooley, said the minister had drawn a false equivalence to justify interference in the editorial independence of public service broadcasters and licensed radio services.
Green Party senator Malcom Noonan said Mr O'Donovan's call to review media coverage of the protests "infringes on the impartiality" of Coimisiún na Meán.
"The minister was clearly trying to suggest that we were all ganging up on them," he said.
Mr Noonan said it was "dangerous territory for the Government and the minister to be straying into".
He said the media had to report "on a fast, evolving situation" in multiple locations around the country".
"I commend them for that," he said.
Meanwhile, Labour TD Conor Sheehan welcomed the Tánaiste's confirmation that there would no investigation into media coverage.
However, he warned that "serious questions remain about the conduct and judgement" of the minister.
"It is deeply concerning that a Government minister would openly call for an investigation into how a public service broadcaster reported on protests," he said.
"That is not the role of a minister in a democratic society and it crosses a very clear line. It speaks to a worrying instinct towards control and interference that has no place in a modern democracy."
Aontú leader Peadar Tóibín said the minister "way overstepped the mark on an authoritarian manner".
He said his party has written a letter to the chair of the media committee asking for Comisiún na Mean and Mr O'Donovan to appear before the committee "straight away".
Mr Dooley said he welcomed Mr Harris' comments.
He said Mr O'Donovan's "behaviour across a number of radio stations yesterday was unacceptable".
"He called into question the professionalism of local and national media journalists," Mr Dooley said.
He added: "His comments in relation to RTÉ were deeply concerning.
"While we welcome the statement by his party leader, we would call on Mr O'Donovan to reflect on his statement and to confirm his acceptance of the independent role of the regulator."
Labour leader Ivana Bacik strongly criticised Mr O'Donovan's statement in the Dáil chamber, declaring "Goodbye Viktor Orbán, hello Patrick O'Donovan".
Social Democrats leader Holly Cairns said the Government is engaged in a "blame game" and the "communications minister is even blaming the media".
Meanwhile, Aontú leader Peadar Tóibín said it was "incredible" that Mr O'Donovan has threatened "press freedom in this country probably for the first time since Eoin O'Duffy himself".
Coimisiún na Meán has confirmed their prior commitment to launch a public consultation on the media service codes later this year.
This will include seeking the public's views on the Code of Fairness, Objectivity and Impartiality in News and Current Affairs across the broadcast media landscape.
Coimisiún na Meán informed Mr O'Donovan that they had received a number of contacts from the public regarding media coverage of the events of last week and would follow up on any formal broadcasting complaints received.
