Taoiseach Micheál Martin has said it would be a mistake at this point to state the final cost of the National Children's Hospital and has vowed not to "play the contractor's game".
His comments follow a report in the Irish Times that Government is braced for a significant increase in the overall bill for the hospital.
Mr Martin tod the Dáil the contractor may submit more financial claims, but the hospital board can contest these and there is a system of arbitration in place.
"I'm not going into any ballpark figures because that would damage the State (and) the taxpayer," he said.
Some €1.1bn has been drawn down to date to fund the building of the hospital, but the Taoiseach conceded the costs would be affected by inflation.
It was important to complete the hospital, which is one of the most important construction projects in the State, the Taoiseach said.
He added that Government would hold firm and would complete the building the hospital, the construction of which began in 2016.
Sinn Féin leader Mary Lou McDonald described the building of the National Children's Hospital as a debacle that could run to a final cost of €2bn.
The Government still does not know what the final cost will be or when the hospital will be built, she said.
Around 100,000 children are on waiting lists but still they do not know when the hospital will be completed and operational, Ms McDonald told the Dáil.
"There has been a focus on your inability to build houses but clearly you are not good at building hospitals either," she said.
Earlier, Sinn Féin's health spokesperson described the hospital as "an absolute disaster from the very start".
Speaking on Today with Claire Byrne, David Cullinane said the hospital had over run costs long before the war in Ukraine and cost-of-living crisis began.
He said the project has to be completed but no clear time frames exist while costs are still question.