Senators Ged Nash and Ivana Bacik made the request as they launched an opposition bill seeking to “address the historic wrong by the State”.
Until 1993, homosexuality was illegal in Ireland, with roughly 2,000 people brought before the courts under the controversial rules over the first seven decades of Irish independence.
Speaking to reporters outside the Dáil, Labour’s equality spokesperson Mr Nash said the reality is these people have never received a formal apology for what happened.
He added that while Enda Kenny was not responsible for the situation he, as sitting Taoiseach, should apologise on the State’s behalf.
“We’ve come a long way in the last 23 years since homosexuality was decriminalised, but we still have a long way to go,” he said.
“What we’re trying to do here is address an historic wrong that was committed through the State.
“Nobody can remove the wrongs, but this is a very important gesture. There are a considerable number of LGBT citizens who haven’t been able to live and love in the climate we have in Ireland today.
“There are probably a couple of thousand, many who are still alive and some who sadly are not.”
Both senators said they are “anxious” to receive all-party backing to the apology plan, which is outlined in the Conviction for Certain Sexual Offences (Apology and Exoneration) Bill 2016.
While admitting they have yet to receive confirmation of formal support for the bill, published yesterday, they do not believe any rival party is likely to be opposed to the move.