AAA-PBP's Paul Murphy is leading calls to get rid of the traditional Christian prayer
There are calls to scrap the prayer currently recited by the Ceann Comhairle at the start of every Dáil sitting.
It comes amid efforts at introducing and agreeing Dáil reform ahead of the formation of a new government.
The Anti Austerity Alliance / People Before Profit TD Paul Murphy and Green Party leader Eamon Ryan are among those calling for the prayer to be scrapped.
It has been suggested that the prayer could be replaced by a minute's silence.
Katherine Zappone told The Irish Times that the Seanad has already introduced a minute's silence alongside the prayer.
Speaking to Newstalk Breakfast, Deputy Murphy said that while this was last item on their list for the Dáil reform agenda, "we do think it's an important issue to be discussed. In some ways it's symbolic of items that are very important - which is that we don't have a separation of church and state in this country".
Deputy Murphy suggested that "we should have a secular society... with everybody free to practice whatever religion they want, without the state promoting or endorsing any one particular religion".
He acknowledged that the upcoming census will likely reveal a majority of the population identify as Christians. However, he said, "a democracy is not a dictatorship of the majority.
"We are about tolerance. I think tolerance would mean we don't have an explicitly religious moment of reflection at the start of the day," he added.