The Labour leader has said his party has drafted a Bill which would remove parliamentary funding from parties refusing to subscribe to the institutions of the State.
Mr Pat Rabbitte said that a minimalist Bill could be brought before the House, adding that the Tánaiste might be interested in making time available for its discussion.
"It would require the very basic preconditions for public funding and would exert them equally across the board in the House . . . In the light of recent events, the taxpayers would be horrified to find their money being intermingled with money from such nefarious causes as we have seen, for the purposes of funding any political party in the State or in this House."
The legislation, he added, "would be a charter to which all of us in this House must subscribe if we want to avail of public resources for our parliamentary duties or political activity".
Ms Harney, who was taking opposition leaders' questions in the absence of the Taoiseach, said she would assume that anyone elected to the House would abide by the Constitution and would support and recognise the Garda and the Army.
"Other issues on funding exist. For example, I would not like it to remain possible for some people to launder money overseas and take it back, perhaps as part of their fundraising activities, into this jurisdiction. We need to examine many issues surrounding the funding of political parties, hopefully in an all-party context."
Earlier, Mr Rabbitte asked if they should consider changing the criteria necessary for a qualifying party.
This, he said, would apply equally to everybody in the House in terms of public funds being made available, and the most basic prerequisite they should require of all democratic parties ought to be fidelity to the nation and loyalty to the State.
Ms Harney said it was not compatible with democracy that some had access to huge amounts of money, the proceeds of crime, to fund a political campaign.
Mr Rabbitte said he was not seeking to entrap the Tánaiste into any specific undertaking.