Fianna Fáil says TDs should be automatically fined a months' wages if they abuse their parliamentary privilege.
But it says it will not seek retrospective punishment against Mary Lou McDonald, after she was found to have abused it herself.
Ms McDonald has described plans by the government to censure her in the Dáil as a diversionary tactic.
It follows reports the government chief whip will write to the Ceann Comhairle, following a finding that she abused Dáil privilege when she named a number of former politicians accusing them of having offshore accounts to evade tax.
All of those named by Deputy McDonald have denied her claims - which she made after receiving a dossier from a whistleblower.
Ms McDonald has said she stands by her actions.
Timmy Dooley of Fianna Fáil says there has never been a situation before where a TD refuses to accept findings made against them.
And he says the Dáil should change the rules so that fines would kick in automatically.