Up to 50,000 passengers were affected by yesterday's strike by signallers in Iarnrod Eireann.
This was the second consecutive day that all mainline rail services were cancelled because traffic signallers withdrew their services. Some 60 freight trains were also cancelled, according to Iarnrod Eireann.
Talks aimed at resolving the dispute will be held between the company, SIPTU and the National Bus and Railworkers' Union at the Labour Court at noon today. "We are all agreed that this is the only possible way forward," said Iarnrod Eireann spokesman Mr Barry Kenny.
If a solution is not found, the strike will resume next Wednesday and will continue for three days.
The 138 signallers are seeking higher basic wages in a new annualised hours agreement.
The continuous disruption to passengers could have long-term implications for the company, Iarnrod Eireann has warned. "It does nothing for passengers' confidence in the service," Mr Kenny said.
He pointed out that the company had just won back its customers after the 10-week strike by drivers during the summer. "Obviously these work stoppages are frustrating customers," he said.
"After decades of neglect, proper investment is finally coming to rail services. We have a record number of people travelling. So it's unfortunate that these stoppages are becoming all too frequent this year." Mr Kenny said he could not put a figure on the daily cost of the signallers' strike but said that it was "considerable", particularly taking into the account the loss of the freight business.
"Nobody wins in this situation. Not the travelling public, not the unions or staff. It is damaging everyone," he said.
It appeared that many potential rail passengers either postponed their journeys or took their cars yesterday, as other public transport systems did not record a major increase in customers. Bus Eireann said there was some increase in passengers on its services. "But it was nothing exceptional" according to Mr Cyril McIntyre, a Bus Eireann spokesman.
However, because the suburban service to Maynooth was not running, Dublin Bus saw a significant increase in passengers using its service covering Maynooth, Leixlip and Lucan.
The DART service from Howth and Malahide to Bray was unaffected by the two-day strike.
Iarnrod Eireann said signallers were being offered a deal which would provide compensation of up to £20,000 for a 20 to 25 per cent reduction in their working week.
However, the NBRU has claimed that its members would still lose £3,000 a year, even with the additional £1,500 offer which was made by the company earlier this week.
The business community has strongly criticised the signallers' actions. The Chambers of Commerce of Ireland said businesses could no longer rely on the rail system because of the continuous disruption.
The Small Firms' Association called for deregulation of the rail service, describing it as a "pitiful excuse for a public transport system".