It emerged this week at the Historical Institutional Abuse (HIA) inquiry that Gardaí (Irish police) knew Smyth was a paedophile as far back as 1973.
Smyth continued to abuse for more than 20 years, until he was jailed in 1994.
Both the main opposition party, Fianna Fáil, and Sinn Féin have called on the government to take action on the case.
Sinn Fein has urged Dublin ministers to set-up an independent judicial review into the HIA revelations.
Fianna Fáil's justice spokesperson, Niall Collins, urged the Irish minister for justice and the head of the police to set up a "mechanism" to address concerns that state agencies failed to act to protect Smyth's victims.
Mr Collins said: "Along with the rest of the country, I have watched with growing dismay and disgust as further details of Brendan Smyth's abuse has been laid bare in the hearings in Banbridge.
"The absolute priority of the Irish state needs to be his victims and ensuring they get the support that they are entitled to."
The Fianna Fáil member added "I have today written to the Garda [police] commissioner and minister for justice and called on them to come forward with a proposed mechanism, at the earliest possible opportunity, to address the concerns of the victims following the revelations that the state appears to have been made aware of the child abuse allegations against Brendan Smyth in 1973 but failed to take action against him until 1994."
Sinn Fein's justice spokesman, Pádraigh Mac Lochlainn, said "This is particularly disturbing because it's those that we trust to protect our society and to look after out laws.
"So, it's particularly serious when it's the Garda Siochána and that's why it needs a serious response from government."
Referring to the HIA inquiry, Mr Mc Lochlainn added: "It is essential that the Irish government assist and complement, in their response, what is taking place in the North."
In a statement on Friday evening, a spokesman for the Department of Justice in Dublin said "The process which is under way in Northern Ireland in relation to historical abuse is ongoing and any conclusions or findings of relevance to this jurisdiction will be studied as and when they are made, taking into account in particular the historical inquiries which have already been carried out in this jurisdiction."
Meanwhile, a man who was sexually abused as a teenager by Fr Brendan Smyth has said Irish police must be held responsible for the abuse he suffered in the 1970s.
Brendan Boland said: "[Gardaí] are equally as responsible as the Catholic Church because they chose not to prosecute him."
Belfast-born Smyth was eventually convicted of more than 100 indecent assaults against children, in both Northern Ireland and the Republic of Ireland.

Olivia Edohasim, nine, died when the black Toyota Auris she was travelling in hit a brick wall on Manchester Road, Altrincham, Greater Manchester, on 7 May.
Police have released two CCTV images of a Citroen and a Range Rover to encourage the drivers to contact them.
Although not involved, police think they may be able to aid the inquiry.
Police said a man, 45, and a girl, 11 - who were also in the car and are believed to be related to Olivia - are still in hospital but are "recovering well".
Police said neither the driver of the Citroen C3 or a dark coloured Range Rover Evoque have come forward to speak to police.
Sgt Brian Orr, of Greater Manchester Police, said: "We don't believe the drivers of these vehicles have done anything wrong or were involved in the collision."
He said new information about where the vehicles were may "jog some memories".
He said: "Moments before the collision the Citroen C3 is seen to be travelling along Stamford Brook Road heading in the direction of Manchester Road."
He said it was then overtaken by the Toyota car Olivia was travelling in near the park entrance of Trafford College.
The Citroen then turned left on to Manchester Road towards Sale.
The driver of the Range Rover Evoque turned right on to Stamford Brook Road from Manchester Road and passed the Dulux building.
Sgt Orr believes the Range Rover driver saw the Toyota Auris overtake the Citroen and flashed the main beam headlights at the Toyota.
The Range Rover then continued along Stamford Brook Road towards Turnbull Road.
The Irish government is facing calls to respond to revelations that police failed to prosecute the paedophile priest, Brendan Smyth, in the 1970s.
[NEXT_CONCEPT]
Police are urging two drivers who may have seen a crash in which a young girl was killed to come forward.