The Seanad has debated the adoption identity bill, which would give about 50,000 adopted people the right to their birth certificate for the first time.
The certificate would list their original name and that of their parents.
Under the bill, adoptees and their parents would also be able to choose whether or not to share contact details.
Philomena Lee, whose son's forced adoption in Ireland in the 1950s inspired the Oscar-nominated film 'Philomena', has called on all senators to support the bill.
The legislation was produced by Senator Averil Power and co-sponsored by Jillian van Turnhout and Fidelma Healy Eames.