Fianna Fáil is calling on the Government to establish a permanent electoral commission, saying it is 'urgently needed'.
Fine Gael has repeatedly pledged to introduce a commission - which would handle issues such as the electoral register, monitoring campaign financing and encouraging members of the public to vote.
Several commentators have called for new regulations for elections and referendums in the wake of the Eighth Amendment vote last week, including around online advertising and election posters.
Fianna Fáil TD James Lawless says "no firm details or timeline" on setting up a commission have been provided despite several recommendations for its introduction.
#8thref has shown need for updated legislation and requirement of an electoral commission. I put this to @campaignforleo and Gov in Dáil calling on them to establish the same. pic.twitter.com/Wxr7mnb2uO
— James Lawless (@lawlessj) May 29, 2018
Deputy Lawless said: "[A commission would] help deal with a number of issues specifically relating to campaigning such as whether limits should be placed on the use of campaign posters, the lack of spending caps in referendum campaigns, whether the broadcasting moratorium is practical given the emergence of social media and the lack of regulation in relation to online campaigning.
"A permanent Electoral Commission independent of the Government and accountable to the Oireachtas is urgently needed. The Government needs to deliver on its commitment in this regard."
Asked about the electoral commission last year, Leo Varadkar responded: "There is no timeframe for it. It is very much a long-term project.
"In the meantime local authorities will continue to manage the electoral register and the Standards in Public Office Commission, SIPO, will continue to carry out its role."
Calls for reform
The latest referendum has prompted calls for reforms in the way votes are held in Ireland.
Earlier this week, the Green Party called for restrictions on referendum and election posters.
Party Cllr Malcolm Noonan argued: "It is clear now that social media is the campaign tool of choice for elections and referenda. Posters are environmentally destructive, visually ugly and a waste of money; in the case of general elections, taxpayers money.
"We are proposing that election and referendum posters be restricted by Local Authorities to designated sites in large towns or cities, where all campaigners and candidates can display their posters."
The RTÉ and Behaviour & Attitudes exit poll conducted last Friday showed only 10% of respondents said the referendum posters influenced them.
Groups such as the Transparent Referendum Initiative, meanwhile, have called for regulations on traditional media to be extended to online campaigning amid concerns about widespread unregistered advertisers.
Concerns have previously been raised about the electoral register, with some suggesting it could be significantly overstated.