The National Bus and Railworkers Union says it does not want the Tranpsort Minister Shane Ross to intervene in the rail strike.
Hundreds of thousands of people had to make alternative plans to get to work and college this morning in the second of five planned strike days with no resolution in sight.
Dermot O'Leary of the NBRU says it needs to be resolved by Irish Rail management and not the minister.
He said: "There is a responsibility on the political arena. Again to be clear, I am not calling for the Minister for Transport to intervene directly in this dispute.
"He has no business in sitting across the table from me, probably wouldn't find him anyway, he's probably out in North Korea or something like that."
Irish Rail, which is already under deep financial strain, is set to lose about €1.5m if staff push through with plans for another three days of stoppages after today.
One of the next planned strikes is on the day of Ireland's World Cup play-off game against Denmark in Dublin next week with the fallout likely to increase pressure on Mr Ross.
The following stoppage is December 8, traditionally the busiest Christmas shopping day of the year.
Iarnrod Eireann management said that as more than 150,000 journeys are made on the network daily and it is not possible to provide alternative transport on dates of industrial action.
No trains have been operating across Intercity, Dart and commuter routes.
Also the result has been huge volumes of traffic in and out of the main cities and a surge in demand for public transport on bus and Luas services.
In some parts of the country where Irish Rail and Bus Eireann share depots, passengers were being dropped off on nearby streets to avoid the crossing of picket lines.
All roads in and out of the capital and other major cities experienced increased delays during the rush hour.
Siptu's organiser Greg Ennis said there had been no contact with Irish Rail or from mediators as the second day of strikes hit.
"There's absolutely no contact. There's nothing going on," he said.
"Our message to the people affected today would be that Siptu represents 170,000 workers, members who are stuck in traffic, stuck in their cars, and our members in Irish Rail are left with no choice but to withdraw their labour.
"They are on strike after 10 years of a pay freeze and carrying significantly more passengers and they have no choice in order to extract a par rise."
Pickets were placed throughout the day at all main Irish Rail stations and Dart lines including Cork, Bray and Fairview.