Indications are that the result of the first count recount for Galway West is expected around 2am tomorrow.
Re-examination and re-counting of all ballot papers is continuing at the count centre in Salthill.
The returning officer says the process will continue until it is completed.
A request by Independent Catherine Connolly for a recount of all ballot papers was granted, after 17 votes separated her from Sean Kyne.
The re-examination and recount of all ballots in Galway West was due began after 4pm this afternoon.
This follows a request from Independent candidate Catherine Connolly after the 13th count concluded shortly after 6am.
At the conclusion of that count, she trailed Fine Gael's Sean Kyne by 17 votes in the race for the final seat.
Fine Gael's Brian Walsh won the third seat after the 12th count, with a surplus of 116 votes.
This left three candidates in contention for last two seats - Ms Connolly, Mr Kyne and Independent Noel Grealish.
With Mr Grealish out of the reach of the remaining two candidates after the 12th count, he was certain to take the fourth seat without reaching the quota.
Since Sunday night, predictions at the count centre focused on a tight battle for the final seat between Ms Connolly and Mr Kyne.
Ms Connolly was 58 votes ahead of Mr Kyne after the 12th count, but 87 transfers from Mr Walsh's surplus edged him ahead in the last count, giving him the last seat.
Both Mr Grealish and Mr Kyne were deemed to be elected without reaching the quota before Connolly requested a recount.
The move means that while five candidates have been deemed to be elected in Galway West, technically none of the seats have been filled, as the returning officer has not declared any candidate to be elected.
Donnelly takes final Wicklow seat
Elsewhere, three Fine Gael TDs, one Labour TD and one Independent TD have been declared elected in Wicklow after 19 counts.
Independent Stephen Donnelly took the last seat after John Brady of Sinn Féin withdrew his request for a recount after he came in 112 votes behind Mr Donnelly.
Simon Harris took the third seat for Fine Gael without reaching the quota and Anne Ferris took the fourth seat for Labour, also without reaching the quota.
The marathon Laois-Offaly count was finally completed in the early hours of this morning, with two Fine Gael TDs, two Fianna Fáil TDs and one Sinn Féin TD being declared elected.
Fine Gael's Charles Flanagan was the first candidate elected on the eighth count. His party colleague Marcella Corcoran Kennedy took the second seat on the 13th count.
Also elected on the 13th count were Fianna Fáil's Barry Cowen, Sinn Féin's Brian Stanley and Fianna Fáil's Sean Fleming - all of whom were elected without reaching the quota.
Former Minister of State John Moloney was eliminated on the 11th count.