Housing Minister Simon Coveney also said he hoped no disagreements would break out in Fine Gael if Mr Kenny did not outline specifics about stepping down at a party meeting tonight.
Chances of a heave diminished after party TD Pat Deering withdrew a threat to lodge a motion of no confidence against Mr Kenny — as long as he quits after St Patrick’s Day.
The developments suggest pressure may be easing on Mr Kenny to step down in the immediate weeks ahead.
Mr Coveney, speaking yesterday in Ballymun, Dublin, said he would not favour any leadership contest beginning before St Patrick’s Day, when Mr Kenny will be in the US.
This would suggest the minister, a top contender to succeed Mr Kenny, is willing to let him stay on for a period, especially as any Fine Gael leadership process may last for weeks.
Mr Coveney said he hoped no disagreements would break out if Mr Kenny fails to give specifics about his resignation this evening at a Fine Gael parliamentary party meeting.
“I think and I hope the party will trust the Taoiseach to put in place a process that will then, presumably after St Patrick’s Day, put a process in place that can allow for an orderly and well-managed transition,” said Mr Coveney.
“Don’t forget we have to have the interests of the country first and foremost in our minds, because Fine Gael is in government, as well as the interests of the party.”
However, asked by the Irish Examiner if the leadership process was something that could run into the Easter period, Mr Coveney replied: “I don’t know, that’s an issue for the Taoiseach.”
If Mr Kenny was still Taoiseach by Easter Monday, on April 17, this would bring him within three days of claiming the title of longest serving Fine Gael Taoiseach, a distinction held by former Taoiseach John A Costello.
A busy schedule in the lead-up to Easter could also delay any formal resignation or the beginning of an election contest.
Mr Kenny’s St Patrick’s Day trip to Washington DC between March 15 and 16 will take place during a trade mission that may last over a week. He is scheduled to attend a meeting of EU leaders in Rome between March 25 and 27, followed by a meeting of the European People’s Party in Malta in late March and an EU leaders’ Brexit meeting in early April.
Meanwhile, senior ministers, including Mr Kenny’s supporters, say the Taoiseach has “gone dark” since the weekend and has told no one as to his intentions. Some have taken that silence as to mean Mr Kenny will give a definitive statement as to his likely departure date.