Taoiseach Micheal Martin has refused calls to intervene in the row over reopening schools for special needs students, and backed under-fire Minister Norma Foley.
Minister Foley and her junior minister Josepha Madigan were criticised by the opposition after Government abandoned plans to reopen schools for children with special needs this Thursday.
The pair were highly critical of teachers' unions in a press release sent on Tuesday night.
It came after unions Forsa and the Irish National Teachers' Organisation (Into) said they had not received sufficient reassurances from the Department of Education that a return to schools was safe.
On Wednesday, Sinn Fein and the Labour Party called on the Taoiseach to intervene in the situation.
Sinn Fein leader Mary Lou McDonald told the Dail: "Minister Foley has twice promised that this would happen and she has twice failed to deliver.
"I have to say the Minister's approach in the media over the past 24 hours, of fingerpointing and seeking to scapegoat SNAs and teachers is fooling nobody," she added.
Labour education spokesman Aodhan O Riordain said: "I put to you Taoiseach that it's now time for you to get involved.
"Quite clearly Minister Foley and Minister Madigan have lost control of the situation.
"Even since last night, we had an extremely ill-advised communication from the department, with quotes from both Ministers in it, which was pointing fingers all over the place."
Mr O Riordain added: "The entire reopening of schools is now in jeopardy because of the bad faith that has been shown by the Ministers in their public comments."
The Taoiseach said that engagement with stakeholders is continuing, and will be led by Minister Foley.
He told the Dail: "I would accept that we need to go forward on a shared basis.
"The Minister for Education will lead that, with her department, and will continue the engagement.
"Today Minister Foley is meeting with many of the representative groups, representing the children and the families of special needs."
He added: "I take your point that we must not allow a divisive fallout from this, in terms of those who provide education services and who look after children.
"I think we must stand back from that."
On Wednesday morning, Ms Foley accused a teachers' union of being "incredibly disingenuous" over claims that it did not instruct its members not to return to schools.
Ms Foley said unions had made it clear they were not happy to accept public health advice.
She made the comments after John Boyle, general secretary of the INTO, insisted the union did not instruct its members not to go to work on Thursday.
On Tuesday night, the Government confirmed its decision not to reopen schools for primary pupils with special needs on Thursday after unions rejected the plans.
The Department of Education said it will "regrettably" not be possible, blaming a lack of co-operation by key unions in the primary sector.
Into and Forsa, which represents 15,000 non-teaching education staff such as special needs assistants, said efforts to reassure staff that it was safe for schools to open limited services to pupils with special education needs (SEN) had failed.
Staff and unions had raised concerns about high levels of infection in the community.
Ms Foley told RTÉ's Morning Ireland that the public health advice given to unions and staff was "categorical and unequivocal".
Asked about Mr Boyle's comments that the vast majority of Into members would have complied with any measures put in place, Ms Foley accused him of being "incredibly disingenuous".
"He made it very clear in the statements that they issued, and indeed with Forsa, that they were not happy to accept the public health advice that was issued to them, that they were not happy to accept all of the measures that were put in place," she added.
"In terms of parental leave and unpaid leave schemes being extended in schools, increased subsidies for full-time childcare for essential workers in education, pregnant teachers and SNAs being allowed to work from home on a temporary basis, the public health advice was categorical, unequivocal, and this is public health advice that came from two experts who have worked hand in hand with Mr Boyle and the other union leaders.
"When the general society is not doing what general society has been asked to do, in terms of reducing contacts and following public health advice, it puts us in a precarious position."
Mr Boyle denied suggestions the union instructed its members not to go back to the classroom.
"It is very, very disappointing that the special education is not restarting tomorrow, face to face," he added.
"I have an understanding that the vast majority of our members would have complied.
"But after our executive meeting last evening I spoke to 300 members, and the big difference is that the numbers of infection (in the) community are 10 times higher now than they were back in December.
"There are very, very legitimate concerns fears and anxieties.
Ms Foley could not confirm when children with special needs will return to school.
Josepha Madigan also clarified a remark she made on RTÉ's Claire Byrne Show on Wednesday morning, in which she compared the situation to the Mother and Baby homes.
She said the comments "pertained to looking after our most vulnerable in society, which children with special educational needs are.
"It was meant as nothing more than that, and at no stage, Ceann Comhairle, would I compare this to very different situations."