Labour Senator Aodhan O'Riordain has apologised for comments he made about the Belfast rape trial.
Jackson's lawyers, KRW Law, had issued an intention to sue Mr O'Riordain for defamation last month.
Paddy Jackson, Stuart Olding, Blaine McIlroy and Rory Harrison were acquitted of all charges following an allegation by a Belfast woman that she had been raped at Mr Jackson's home.
The ruling drew a massive amount of commentary online, including a tweet from Senator Aodhan O'Riordain which Mr Jackson and his legal team judged to be defamatory.
Mr Jackson's lawyers issued a notice of intention to sue Mr O'Riordain.
This morning the Senator apologised for his tweet.
He said it was not designed to suggest that Mr Jackson or any of the other accused men were guilty, or that the jury got it wrong.
He apologised for any suggestion to the contrary and said he accepts he was not privy to all the evidence put before the jury during the trial.
His statement this morning read: "My tweet of 28 March concerning the Belfast rape trial was not designed or intended to suggest that either Paddy Jackson or any of the other accused men were guilty or that the jury got it wrong.
"I apologise for any suggestion to the contrary. I accept that I was not privy to all the evidence put before the jury during the trial.
"I will not be making any further comment."
A statement from lawyers representing Mr Jackson on March 30 said they are to issue notice of intention to sue Senator Ó Ríordáin for "defamatory comments made by him in the immediate aftermath of the jury's verdict".
KRW Law said the legal action relates to a tweet sent to a number of other persons before it was eventually taken down.
It added that Mr Jackson "now finds himself resorting to the Civil Courts in order to seek protective action".
Senior associate of KRW Law solicitors, Marie Hans, said: "I can confirm we have issued pre-action libel correspondence against a named Senator in the Republic of Ireland.
"The legal action related to a tweet sent to a number of others persons before it was eventually taken down."
She added: "We will not hesitate to repeat similar legal action against anyone who deliberately or otherwise, sees fit to attack our client. We are examining carefully every item of social media commentary which seeks to challenge the integrity of the jury's full endorsement of our client's innocence.
"High Court proceedings will issue shortly in both Belfast and Dublin."