The contractor responsible for the National Children's Hospital has said it will opt out from the project if the board responsible for it wishes to re-tender the contract.
BAM Chief Executive Theo Cullinane said if the board wished to "procure the work in some other way" they will "co-operate with them to facilitate this option".
However, BAM said that the company "will continue its commitment to the new children's hospital and the confidence of all parties involved is a vital requirement for the company".
In a statement, the Kildare-based firm said that it did not benefit inappropriately from the tender process for the project.
The company said much of the commentary surrounding the tendering process is "based on incomplete and inaccurate information".
It said it will engage with PwC to ensure all relevant facts are disclosed.
The company has also said it has written to Taoiseach Leo Varadkar, requesting him to clarify that comments he made in the Dáil on Tuesday 12 February were not referring to BAM.
PwC is conducting a review of cost overruns at the hospital.
In a statement this evening, the National Paediatric Hospital Development Board said it was "committed" to delivering the new children's hospital.
Responding to the BAM statement, a Government spokesman said that the Taoiseach "did not reference any specific company in the Dáil".
He added: "The Government is not satisfied with several aspects of how the new national children's hospital project has been delivered.
"There is understandable public concern about the matter. For this reason, PwC has been commissioned to carry out an independent examination.
"He hopes and trusts that all parties and contractors will co-operate fully with it."
Fianna Fáil's health spokesman Stephen Donnelly has said it appears that BAM's offer has been made in good faith.
He said the Government should evaluate it in the context of delivering the best possible hospital within an acceptable cost.
The Wicklow TD said it could provide new opportunities for the Government to work with BAM and drive down costs at the hospital.
Sinn Féin's Health Spokesperson Louise O'Reilly has called on the Taoiseach and Minister for Health Simon Harris to hold an urgent meeting with BAM and assess what "cost recovery" can be secured regarding the hospital.
She said the Joint Oireachtas Committee on Health also needed to hear from both BAM executives and all members of the National Paediatric Hospital Development Board.
Independents4Change TD Mick Wallace has said that the Government should accept BAM's offer to re-tender.
Mr Wallace told RTÉ News: "They should take-up their offer, big time." He said he believed the Government might be reluctant to re-tender on the basis that it would be perceived as an admission that they 'messed-up.'
However the Wexford TD said: "It's better to do the right thing now - and that's re-tender. The problems now associated with hospital contract are not going to disappear."
Green Party Leader Eamon Ryan said the BAM offer would have to be welcomed if it translated into savings for the taxpayer.
He said the whole debacle illustrated that the tendering process had been "deeply flawed."
Mr Ryan said the Government was clearly in "crisis management mode."
Labour's Health spokesman Alan Kelly has said the Government should "strongly consider" BAM's offer.
The Tipperary TD said this re-evaluation could be undertaken by the Government over the next six months while Phase 1 of the contract is being completed.
He said this would mean that it would not delay the construction of the landmark facility.
The chair of the Joint Oireachtas Committee on Health, Dr Michael Harty, has said the BAM statement opens-up the possibility of the hospital being located away from St James' Hospital to a green-field site.
The Independent TD told RTÉ that the offer by BAM to re-open the contract would also be judged on how much cheaper, if at all, it would be to complete the NCH.