Sinn Féin leader Mary Lou McDonald says Minister Simon Coveney should be sacked due to the Katherine Zappone controversy.
It follows the Foreign Minister's appearance before an Oireachtas committee on Tuesday.
Mr Coveney said the creation of a Special Envoy role at the United Nations was being explored by his department, before he asked Ms Zappone on March 3rd if it was something she would be interested in.
But he added he should have been clearer at the time it was not a job offer, and acknowledged he "made mistakes" - including giving "sloppy" answers to the Oireachtas.
Ms McDonald says her party will act if no action is taken on the Government side.
"It's now eight weeks into this crisis, and over the eight weeks we've heard Minister Coveney change his story - but stick to a version of events that is wholly incredible.
"He kept information from the Taoiseach for a number of months, he destroyed departmental records which he's obliged to protect and keep under law.
"And I think this behaviour is not of the standard that would be expected of any minister of Government, and I know that the Taoiseach has said that Minister Coveney was wrong.
"So there needs to be accountability now at the heart of Government, there needs to be an appropriate sanction for Simon Coveney, the Taoiseach needs to act.
"I think he needs to come out today and set out, very clearly, the course of action that he proposes to take.
"And in the event that he is not prepared to act, well then Sinn Féin will."
'Ball is at the foot of Micheál Martin'
Asked if she thinks Taoiseach Micheál Martin should sack Minister Coveney, she said: "I do.
"As I say I think it's very hard to see how the minister can remain in his position, given that we have had eight weeks of this controversy, of just herculean efforts to cover tracks in a scenario where clearly a job was created for a friend and former colleague."
Ms McDonald says she cannot see how Minister Coveney can stay in his position.
"It's hard to see how Minister Coveney can stay on, given all that has transpired over the last eight weeks."
She also claims there is "nobody who believes the version of events that has been set out by Minister Coveney".
She says while her party could still table a motion of no confidence, the next move is up to Mr Martin.
"I'm saying in the first instance... that the Taoiseach needs to act, he's the head of Government - not me.
"The timeline now is today for the Taoiseach to come out as head of Government, and set out very clearly what he proposes to do in respect of a minister in his Government that has behaved in this way.
"The ball is now at the foot of Micheál Martin - what will the Taoiseach do, that's the question for today."