The Government has been told to "do the right thing" and engage without preconditions with striking nurses.
Nurses and midwives are currently taking part in a third day of industrial action over pay and conditions and are set to strike for three consecutive days next week.
Speaking in the Dáil Health Minister Simon Harris said the Government is eager to come to "a fair and satisfactory solution" but it would have to one that preserves the integrity of all elements of the public sector pay agreement reached last year.
Addressing a group of nurses who watched the debate from the public gallery, Solidarity PBP TD Mick Barry encouraged them to "keep your nerve" and keep up the pressure on the picket line.
Mr Harris said the current public sector agreement commits to seeing significant increases in pay by 2020 and will mean many will see wage increase of between 2% and 2.5% by the end of this year.
"Just because something is difficult does not mean that we give up. Far from it. There have been repeated attempts to resolve this dispute. None of which have borne fruit yet. I stress ‘yet’. I do believe that there are solutions to be found but it will require imagination and innovation on both sides."
The Minister said he is willing to engage in talks on the range of workplace related issues other than pay to try to resolve the dispute.
He solution will not be found on the picket line or in the Dáil but through industrial relations mechanisms such as the Labour court.
But TDs from across the opposition demanded that the Government enter talks without preconditions with Labour TD Alan Kelly asking "what's to be lost" in doing so?
"It's going to happen anyway, it might as well happen now," he said.
Sinn Féin health spokesperson Louise O'Reilly said nurses working abroad want to be given a reason to come home.
"Pay them decently, stop educating our nurses and our midwives to work in health services elsewhere," she said.
Ms O'Reilly said Mr Harris now has the opportunity to "do the right thing" and enter talks but said "there is no point everyone sitting around a table looking at each other when there is no will to resolve the dispute."
Fianna Fáil's Stephen Donnelly said health care professionals are now at their wits' end while his party colleague Barry Cowen said patients and the public are now suffering.
Dr Michael Harty said the strike is a result of a "failure to anticipate and deal with the frustration that nurses have" and said there is now a need for massive reform of the health system.