Update 6.01pm:Taoiseach Leo Varadkar has warned that pay rises for rail workers should wait until investment is made to the fleet and infrastructure.
Tens of thousands of commuters and transport users faced morning and evening chaos on the roads as Irish Rail staff held a second day of walk-outs, with another three days of action planned.
However, the Taoiseach warned that money should first be spent on safety, increasing line speed and buying more carriages to improve the service and respond to climate change.
"That means any additional, or at least the vast majority of additional, revenue that goes into the companies ... should go into improving the services, making them safer and making them better rather than pay increases," he said.
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.
The next planned strike 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 Minister for Transport, Tourism and Sport Shane Ross.
The following stoppage is December 8, traditionally the busiest Christmas shopping day of the year.
Siptu accused Irish Rail of sending staff letters which could be seen as threatening their livelihoods after chief executive David Franks wrote saying the dispute could damage the company and hit workers' pay.
Union organiser Greg Ennis said: "Such an approach has only strengthened the resolve and commitment of our members to continue their industrial action until all sides agree a just resolution."
No trains operated across Intercity, Dart and commuter routes.
The result was 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 hours, with some areas around Dublin seeing car users in vehicles for an hour longer than normal.
Mr 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.
Pickets were placed throughout the day at all main Irish Rail stations and Dart lines including Bray and Fairview, and staff were keen to apologise for the disruption.
Martin Fox, a driver on the Galway to Dublin and Limerick lines for more than 12 years, said: "The last thing we want to do is inconvenience the public. We apologise to them. But we feel that we are left with no choice."
Mr Fox said he thought a deal was close to being agreed during negotiations with mediators last month but he blamed Irish Rail for pulling the plug on it.
He added: "We have a minister for transport who seems more interested in tweeting about Manchester United and problems in North Korea.
"He's conspicuous by his absence in this dispute. He does not seem to want to get involved."
AA Roadwatch reported the main arteries into Dublin saw significant increases in traffic including the M4, M7, M3 and the Rock Road and Stillorgan Roads, and also from Darndale into Dublin city.
Elaine O'Sullivan, editor of AA Roadwatch, said: "The daily commute started a bit earlier.
"We noticed an increase in traffic volumes from about 6.45am but the busiest times were between eight and nine as expected.
"It was very heavy on all the main arteries into Dublin."
AA Roadwatch also said there was increased traffic in Galway and Cork, and in Limerick where the volumes increased later in the morning.
Earlier: Tens of thousands of rail passengers are facing a longer than usual journey home this evening.
A 24-hour strike at Irish Rail is continuing - with three more planned days of industrial action in the coming weeks.
Management has asked unions to engage in more talks.
"We don't want to be here and we feel for the general public, you know - but we have to stand up for our rights too," a rail worker at Heuston Station said.
The Taoiseach has called on all sides in the rail dispute to meet at the Labour Court and resolve their strike.
Thousands of commuters are affected by today's work stoppage with the third day of action planned for next Tuesday.
Leo Varadkar said Irish Rail workers did not face any pay cuts during the recession and the industrial relations institutes are the places to make their pay rise claims.
"The way Government intervenes in these disputes is not through ministerial intervention. That has not been the case for a very long time," he said.
"I know that the Labour Court and the WRC will be willing to intervene in this dispute if they believe there's a suffiicent willingness from both management and unions to come to an agreement.
"I hope that willingness exists and if it does I'm sure there will be a Labour Court intervention."