The Taoiseach has been accused of claiming Mary Lou McDonald was “telling lies” in a testy exchange during a debate about housing issues.
Ms McDonald said that Micheal Martin had accused her of telling lies while speaking in Irish, and asked him to withdraw the remark.
Ceann Comhairle Verona Murphy does not have Irish and said she could not rule on something she did not hear.
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Mr Martin told the Dail he never called the Sinn Fein leader a liar.
Ms McDonald accused the Fianna Fail leader of “taking advantage” of the matter and that he did call her a liar.
“I would like him to remove that from the record,” she added.
Mr Martin was heard saying in his reply to Ms McDonald during a debate on housing: “Ta an Teachta Dala ag insint breaga aris.”
It translates to: “The TD is telling lies again”.
Under Dail rules, entitled Salient Rulings of the Chair, it states that allegations which have been ruled as disorderly are that a TD was guilty of being deceitful.
Addressing Mr Martin, Ms Murphy said: “I would ask you to withdraw, if you made those remarks. I am not aware.
“Please resume your seat.
“I can’t rule on what I didn’t hear. I accept that you believe it was said. The Taosieach said he hasn’t said it. We can look back.”
Sinn Fein TD Pearse Doherty said: “He took advantage of the fact that CC has no Irish. And you are taking advantage of the Irish language.”
“Taoiseach, if you use the words, would you withdraw them? Would you withdraw them?
“If you use them, Taoiseach, I didn’t ask you to stand up. I ask you specifically to withdraw the words if you use them.”
Addressing Ms McDonald, Ms Murphy said: “I would say to the leader of Sinn Fein that if she wishes to make a complaint in writing, we will deal with it.”
Mr Doherty then said: “I am sure the officials can assist the Ceann Comhairle with regard to what was said at this point in time.
“The officials are there to help the Ceann Comhairle and to interpret what was said in Irish.”
A spokesman for the Taoiseach later said Mr Martin did not intend to withdraw the remarks, characterising the row as a “distraction tactic by Sinn Fein”.
The spokesman said the comments came after days of the opposition accusing members of Government of misleading people.
Asked if Mr Martin had spoken in Irish to avoid being censured by the Ceann Comhairle, the spokesman said the language is used in the Dail “all the time”.
He added that people were always accusing each other of misleading statements or twisting facts “in a very rough-and-tumble Dail”.
Ms McDonald sent a letter to Ms Murphy on Wednesday evening requesting that she “follow up formally with An Taoiseach and ensure that he now does withdraw the remark”.
“In his response and speaking Irish, An Taoiseach made a baseless accusation that I was ‘telling lies’. I absolutely refuse that this was the case,” she said.
“My colleague deputy Pearse Doherty intervened to make a point of order and draw this to your attention while in the chair requesting that you call on the Taoiseach to withdraw the accusation.
“I am now writing to request that you follow up formally with An Taoiseach and ensure that he now does withdraw the remark in the Dail at the earliest opportunity.”