It has been confirmed there will be no votes for Taoiseach when the Dáil sits next week.
The Dáil is due to sit for a second time next Thursday.
However, the Business Committee has decided there would be no point in trying to elect a Taoiseach - as there is no chance of a government being formed in that time.
One member of the committee said it would only be playing games, and that the Dáil isn't there to run a popularity contest.
The first votes for Taoiseach were held when the 33rd Dáil met for the first time last week.
While Sinn Féin leader Mary Lou McDonald receive the most votes - 45 compared to Micheál Martin's 41 - it was still far short of the 81 votes needed to secure a majority in the chamber.
Sinn Féin's Pearse Doherty this afternoon said it's disappointing that there is not going to be another vote next week.
He observed: "Not that I expect that there would be an outcome to that process... but at least it's a marking point, it's a stage in the process.
"Failure to have that [vote] to me withdraws momentum."
Instead of votes for Taoiseach, the Dáil will hear statements on the upcoming EU Council meeting and the coronavirus.
The decision means the process of forming a government could be even longer than expected.
No new Taoiseach being elected next week means Leo Varadkar will travel to Washington for the St Patrick's Day meeting in the White House.
If serious negotiations on forming a government only start after that, it could be well after Easter before a new Taoiseach and cabinet is in place
Talks have been continuing this week between various parties as both Micheál Martin and Mary Lou McDonald continue their separate efforts to pull together the necessary numbers for a government.
