Ceann Comhairle Seán Barrett is to contact Fianna Fáil leader Micheal Martin over the party's concerns about remarks he made last week in an RTÉ Radio interview.
Mr Martin was informed that Mr Barrett will be returning to Ireland this evening and will be in contact with him.
In a statement earlier, Mr Barrett said he accepted the Opposition was entitled to question his decision to rule out a Dáil debate on an inquiry into allegations of garda malpractice in the Cavan/Monaghan division.
However, he failed to withdraw the claim that the Opposition had sought to undermine him.
Fianna Fáil TD Barry Cowen said Mr Barrett had clearly gone some way towards addressing their concerns but still had a distance to go before the party made a decision on whether to table a motion of no confidence in him.
Mr Cowen said he understood the Ceann Comhairle would be in touch with Mr Martin to further clarify the situation and Fianna Fáil would then consider their position at a parliamentary meeting tomorrow night.
In the statement, Mr Barrett said: "In relation to my interview with RTÉ on Friday last, perhaps in the heat of the moment during that interview, I may have given the impression that the Opposition were not entitled to question my decision as to why a debate was not allowed.
"Of course, I accept that they are entitled to question my decision.
“However, I will state that I made the decision after careful consideration in the best interest of the Oireachtas and the taxpayer."
The statement - while conciliatory in tone - did not address the central objection to his remarks from Fianna Fáil and Sinn Féin, and his charge that the parties were trying to undermine his position.
Tanaiste Joan Burton said the Ceann Comhairle had set down a clear marker about his appreciation and respect for the Opposition.
"I saw the statement which the Ceann Comhairle issued and I think it's good he has put on record his very strong appreciation of the role of the Opposition in raising matters in the Dáil and being able to debate them in full."
She said the Government had been "anxious" to have a Dáil debate on the terms of reference of the Guerin inquiry and had structured Dáil business to provide for it.
However, Mr Barrett made the ultimate decision and decided it was not possible.
Earlier, Fianna Fáil chief whip Seán Ó Fearghaíl said the statement from Mr Barrett did not go far enough.
He said was was needed was a clear and unambiguous withdrawal of the claim that his party had sought to undermine the Ceann Comhairle.
People Before Profit TD Richard Boyd Barrett said he believed there would be unanimous support from independents if a motion of no confidence was put down.
He told the News At One that he welcomed the statement from the Ceann Comhairle but that a full and satisfactory explanation of the decision was still needed.
He added that anything that led to the closing down of political debate in the Dáil was a problem.
Earlier, Mr Ó Fearghaíl said his party fundamentally disagreed with Mr Barrett's decision as it had shut down debate in an unprecedented way.
He said all previous terms of reference had been debated.
The Minister for the Enviornment, Alan Kelly, said this afternoon he supported Mr Barrett.
He said Mr Barrett had a "very difficult job" and he had to make a "very difficult decision".
However, he said in the future, if standing orders needed to changed, then it should be done.
"We need to ensure that at all times, the parliament of the land, which is elected democratically by the people, can talk and discuss any issue that it feels necessary," he added.
Meanwhile, Minister for Finance Michael Noonan said Mr Barrett had been fair and unbiased in his role, adding that he hoped the situation can be resolved.
He said the Ceann Comhairle took legal advice from his officials and he was advised the best course of action was to proceed on the Guerin-advised inquiry and its terms of reference without a Dáil debate, and he was fully entitled to do that in accordance with the independence of his office.
Speaking on RTÉ's Morning Ireland, Sinn Féin deputy leader Mary Lou McDonald said she personally did not have confidence in the Ceann Comhairle.
She said his decision not to allow a debate on the terms of reference for the Cavan/Monaghan garda division inquiry was "strange and troubling".
