The Taoiseach Enda Kenny is insisting he will deal with the issue of his leadership of the country on Wednesday.

It is understood the issue was raised briefly at the Cabinet meeting on Tuesday morning.

But Mr Kenny told the gathering he would deal with it at the parliamentary party meeting tomorrow.

In the Dáil this afternoon, Fianna Fáil leader Micheál Martin and Sinn féín President Gerry Adams were among those who tried to get the Taoiseach to comment.

However, Enda Kenny refused to be drawn on his future leadership plans.

Amid speculation over Simon Harris' intention to enter any potential leadership contest, the Taoiseach said: "Let me say that young Minister Harris is enjoying the greatest honour of his career in dealing with the Department of Health".

Heading into Cabinet meeting earlier, Independent Alliance super junior minister Finian McGrath said the issue needed to be dealt with.

"We need a speedy conclusion to that particular debate so that we can all focus on the day job.

"The leadership issue is a bit of a distraction, but it needs to be resolved and I'm confident the Taoiseach will resolve it over the next couple of days."

"A bit of a distraction"

For its part, Fianna Fáil said the Government needs to get on with its job.

Finance spokesman Michael McGrath: "The relevance of the Fine Gael leadership is how it impacts on the day-to-day workings of Government, and for us that is the critical issue.

"We're not going to stand back and facilitate a Government that develops into a circus.

"The leadership issue is a bit of a distraction, but it needs to be resolved and I'm confident the Taoiseach will resolve it over the next couple of day."

Leo Varadkar (left) and Simon Coveney (right) at the Fine Gael Think-In in 2008 | Image: RollingNews.ie

Speculation continues as to who might be challengers for the party leadership.

Simon Harris seemed to outline his credentials for leadership last night - dismissing the suggestion that he is too young to run.

Speaking Tuesday, Minister Harris said: "I've made no decision to running or not running.

"But I always do make the point that I think age is immaterial. I've worked extremely hard in government, in a range of positions [...] I think people should be judged on their vision for the country, and not on an age on a birth cert."

The Tánaiste Frances Fitzgerald and Education Minister Richard Bruton have also refused to rule themselves out of a contest.

The Dáil resumes this afternoon and it is unlikely Mr Kenny will get through the day without somebody raising his future with him.

On Monday, Mr Coveney called for TDs to back off from Mr Kenny - saying the Taoiseach needs "time and space" to follow through on an orderly change of leadership.

However, it is unlikely that any potential successors will announce their intention to run for leader until after Mr Kenny addresses the party on Wednesday evening.