Around half of the total number of ballot papers cast in the Midlands-North-West constituency have been rechecked.
First preference bundles for Luke 'Ming' Flanagan, Mairead McGuinness and Matt Carthy have been reviewed.
Count staff are checking each vote to make sure it has a Number 1 for the candidate in question.
No major discrepancies have been found among 330,000 papers. So far only a handful of votes have been found to have been placed incorrectly in bundles.
Supporters of Independent outgoing MEP Marian Harkin say there will be no material change to the 275 vote gap between her and Pat 'the Cope' Gallagher as a result of the recheck.
Around 70 volunteers travelled to the count centre in Castlebar to monitor the process, after the Harkin campaign issued a call for assistance earlier today.
Mr Flanagan is also helping out, along with key members of his campaign team.
Fianna Fáil said it is particularly keen to view the ballot papers of its other candidate Thomas Byrne.
After his elimination, 16,013 votes were not transferable.
The party is hoping that some discrepancy in this regard may assist Mr Gallagher.
The recheck is progressing faster than was initially thought.
Returning Officer Fintan Murphy said the way in which count staff have approached their task since votes were sorted on Saturday morning has made the job more straightforward today.
It is hoped that the recheck may conclude late tonight.
A decision on whether to call a full recount at that stage would rest with the individual candidates.
The decision to do a recheck was welcomed by both candidates last night.
Ms Harkin said if she was the one trailing, she would want a recheck.
She said: "If I was in Pat's position I'd be looking for this and that's why I'm quite happy that happens because this is the democratic process.
"We have to be sure that it is right and whoever wins at the end of the day that's it. But we must make sure that it is right. I believe it will take more than one day."
Mr Gallagher said the recheck was necessary because only the slimmest of margins separated them.
He said: "I welcome the offer by the returning officer to commence a recheck."
"Of course, we have to take into consideration that the margin is just 275, which is less than 0.05%, and in the circumstances I am very pleased that the returning officer has done this."
FG's Fayne takes final seat in Dún Laoghaire
The Dún Laoghaire LEA recount is finally complete after ten hours of counting today.
Fine Gael candidate Mary Fayne was the eighth and final candidate elected for the LEA.
She held off sitting Labour Councillor Jane Dillon Byrne, who had closed to within nine votes during the recount.
Ms Dillon Byrne, who has been a councillor in the Dún Laoghaire area for 40 years, requested the recount on Sunday evening after losing out on the last seat by 18 votes.
After the result was announced by Deputy Returning Officer Tom McHugh, Ms Dillon Byrne said she has not decided if this would be her final time contesting local elections.
She thanked her family and colleagues for their support throughout a "tough campaign".
Ms Fayne is the third Fine Gael candidate to be elected for the Dún Laoghaire LEA, joining John Bailey who topped the poll and Patricia Stewart, who was also elected.
Ms Dillon Byrne's elimination means that Dún Laoghaire will be the only LEA in Dún Laoghaire Rathdown where the Labour Party will have no representation on the new council.
Fianna Fáil wins most local authority seats
So far, 943 of the 949 seats have been filled and 29 of the 31 councils have declared final results.
Fianna Fáil has ended up with the most seats, ahead of Independents and Others.
The Local Election results are:
- Fianna Fáil 266 seats (25.3%)
- Independents and Others 237 seats (28.3%)
- Fine Gael 232 seats (24%)
- Sinn Féin 157 seats (15.2%)
- Labour 51 seats (7.2%)