Opposition TDs have urged Michael D Higgins not to sign the controversial mother and baby home legislation.
The legislation allows a database created by the Commission of Investigation into Mother and Baby Homes to be sealed for 30 years.
While the Government has insisted the Bill provides access for survivors of mother and baby homes, this claim has been disputed by opposition TDs, survivors and legal experts and academics.
The Dail passed the Bill by 78 votes to 67 on Thursday night.
The Mother and Baby Homes Commission, which was established by the Government five years ago, is to publish its findings of a lengthy investigation next week.
As part of its work, the Commission created a database of 60,000 records containing details of those who passed through the mother and baby homes.
The Commission of Investigation (Mother and Baby Homes and certain related matters) Records and another Matter Bill is to be signed into law by President Michael D Higgins.
However, opposition TDs have urged the president to convene a meeting of the Council of State - a mechanism used to refer legislation to the Supreme Court to establish if it breaches the Constitution.
It comes as more than 140,000 people signed a petition calling for the seal to be removed on the mother and baby home documents.
The petition was set up by adoptee identity rights group Aitheantas on Friday.
People before Profit TD Brid Smith was among those calling on the president not to sign the Bill.
"The Government must reconsider the sealing of archives," she said.
"It is clear from the debate and subsequent information that the (Children's) Minister (Roderick O'Gorman) and Government have no clear idea what information is being sealed and what records might still be available to survivors in the future.
"This is deeply traumatic for the families and survivors and the Government need to to change direction on this before compounding the trauma and hurt to victims after the decades of state abuse and collusion with religious orders at the heart of this scandal."
Sinn Fein's justice spokesman Martin Kenny said it is likely the Government will face legal action.
"The truth is it should never be in this position. If any of the amendments that opposition TDs put forward were accepted by the minister (Mr O'Gorman) then we could have avoided this situation," he told RTÉ's The Week In Politics programme.
"We were faced with Hobson's choice - either it would be sealed for 30 years or it would be destroyed, which is not true.
"This crisis has been bubbling under the surface and nothing has been done about and then at the last minute it was rushed through.
"It shows how out of touch they are. There is seething anger in so many people. There is still time to go back and look at it again."
Independent TD Michael Fitzmaurice described it as one of the "worst pieces of legislation" passed by the Dail.
"This is a dark time in Irish life and we need to do this right as public representatives," he added.
"Opposition TDs were just cast aside. We need to get this right and treat people with honesty and fairness.
"I would ask Michael D Higgins is do not sign it."
Tanaiste Leo Varadkar insisted the legislation will not see the database sealed for 30 years.
"There has been a huge outpour of emotion and empathy and I think some genuine people have got the message wrong about this," he said.
"The database is not going to be sealed and put away for 30 years - it's being protected and for people who want to have access to their information we will make sure they get access to that information.
"We are not going to allow a situation where secret of past are allowed to be hidden."