Fine Gael representatives including Michael Noonan, leader Enda Kenny, Frances Fitzgerald, Leo Varadkar and Simon Harris.RollingNews

Ireland may be facing an early return to the polling-booth unless a government can be elected in the near future. Political tension is rising in advance of Thursday's meeting of the Dáil which is expected to vote on the position of Taoiseach (Prime Minister).

In the aftermath of the last election on February 26, Enda Kenny holds the title of Acting Taoiseach and he is expected to be proposed by Fine Gael party colleagues to head up a new government at Thursday's Dáil sitting (Irish House of Representatives).

Fianna Fáil is also offering to lead the next government but, with 44 TDs, the party has six fewer Dáil seats than Fine Gael. If Fianna Fáil abstains and Kenny can gain the support of eight TDs outside his own party, then he will win the vote.

Last Wednesday, Kenny caused general surprise when he proposed in a meeting with Fianna Fáil leader Micheál Martin and proposed that the two parties should join together with a number of Independent TDs to form a "partnership" coalition government.

The suggestion was emphatically rejected by Fianna Fáil at a meeting of its parliamentary party the following day but Martin indicated that he would be willing to back a Fine Gael-led minority administration from the opposition benches or, if that was not possible, to lead such a government himself.

➜ WATCH: Micheál Martin TD addresses the media. The best interests of the Irish people are not served by a Government made up of Fianna Fáil & Fine Gael.

Posted by Fianna Fáil on Déardaoin, 7 Aibreán 2016

There has been some criticism of Fianna Fáil for rejecting Kenny's proposal but Martin and his party may have grounds for believing that they could be the dominant force after the next general election.

However, Fianna Fáil will be keen to ensure that the ballot does not take place in the near future because a very similar result to the last one would be expected and Martin's party might also be blamed by voters for causing the second election to be held at such an early stage.

Sinn Féin won 23 seats in the last election and, if Fianna Fáil went into government, Gerry Adams would be leading the main opposition party.

Newly-elected Sinn Féin TD for the north Dublin constituency of Fingal, Louise O'Reilly said: “Fianna Fáil would rather be beholden to a Fine Gael government and give up potential power-sharing, rather than allow Sinn Féin to become the largest party in opposition."

Read more - Exclusive: Gerry Adams on 1916 and the counter-revolution that followed

The coming days are expected to see intense activity behind the scenes as Independents discuss terms under which they might lend their support to Kenny or Martin for the position of Taoiseach.

The general expectation is that Kenny will be voted into the job and proceed to form a government thereafter which is likely to include a number of ministerial appointees from the ranks of the Independents.

However, such a minority administration is not likely to last very long and it is expected that Fianna Fáil will be seeking to bring it down at an opportune moment, perhaps this time next year.

Acting Minister for Health, Leo Varadkar of Fine Gael said a minority government led by his party would need a written agreement from Fianna Fáil to give it support from the opposition side of the House.

“I think at the very least it would have to have a written agreement – on how long it would last, on key policy issues and also support for budgets and confidence votes,” he told RTE's 'Morning Ireland' programme.

Acting Minister of Health Leo Varadkar.

Acting Minister of Health Leo Varadkar.

“In the absence of that I don’t think it would last. More importantly, worse than that, I don’t think it would be a good government, because [it] would be always looking over its shoulder.

“A government like that will put off important decisions, will not think long-term and will be forced into constant climb-downs, often doing the wrong thing, but having to do that just to survive. That would not be a good outcome for the country and certainly not for the party either, but it's the country that matters most."

Newly-elected Fianna Fáil TD for Dublin West, Jack Chambers told RTE's "News at One" that, if the Independents opted to support Kenny instead of Martin, then "Fianna Fail are willing to abstain next Thursday".

Meanwhile, Acting Taoiseach Enda Kenny has invited Independent TDs and Fianna Fáil leader Micheál Martin to a meeting.

It is believed the meeting would focus on terms for a Fine Gael-led minority government.

One of the non-party groupings, the Independent Alliance, is seeking a guarantee from Fine Gael and Fianna Fáil that a minority administration would be allowed stay in office for at least three annual Budgets.

Members of the Alliance include Shane Ross TD and Finian McGrath TD.