Sinn Féin will pull the plug on the Ireland South recount if it becomes clear they are not making up the gap in votes, Mary Lou McDonald has said.
The party asked for a full recount after just 326 votes separated Liadh Ní Riada and Green Party senator Grace O'Sullivan following a recheck of papers.
The recount in the 12-county constituency will start next Tuesday and is expected to take 28 working days which would have implications on all of Ireland South's MEPs as they would miss a number of important deadlines including the election of the new parliament president.
While Fine Gael's Sean Kelly and Fianna Fáil's Billy Kelleher were deemed elected in the initial count, they will not be able to attend parliament until the count concludes.
No one is deemed an elected an MEP until all seats have been filled.
A spokesperson for the European Parliament said: "The first deadline from a European Parliament point of view is June 24. On that date, political groups must confirm their composition and membership.
"The new Parliament then takes office from July 2 and there would be important votes that week, such as the election of the new President of Parliament."
Ms McDonald said her party doesn't want to "prolong the agony or postpone the ecstasy" but Sinn Féin wants to be sure that the outcome of the vote is accurate.
"The contest in Ireland South was very, very tight," she said, adding that the difference in votes is equivalent to around five ballots in a local elections.
However, speaking on RTÉ's Sean O'Rourke programme, Ms McDonald said: "How recounts work is the recount begins and then obviously you take stock as the process unfolds.
"If it becomes apparent that the result isn't going to change then of course at that stage then the counting will end," she said.
Asked about Sinn Féin's poor performance in the local elections, Ms McDonald suggested there is a detachment from politics in certain sections of society.
"I am not sure that you can attribute it to any single one thing," she said.
The delay in the Ireland South count has led to some calls for the introduction of an electronic system with Taoiseach Leo Varadkar suggesting that vote counting machines could be brought in Scotland.
However, he stopped short of arguing in favour of introducing e-voting.
A recent survey found that 52% of those asked would like to have the option of casting their vote by electronic means.
The Pure Telecom survey also revealed that 27% of people believe our traditional polling methods are outdated.
Pure Telecom CEO Paul Connell said: “Our research shows that Irish adults are very open to the idea of voting by electronic means.
"In the digital age, people are used to being able to complete tasks with the touch of a button or screen – so electronic voting appeals to them."