The NBRU is also considering strike action at the company
Two other unions are to ballot their members for industrial action at Irish Rail after the NBRU announced plans to do so.
SIPTU and Unite claim they have been left with no choice.
Talks between the National Bus and Rail Union (NBRU) and Iarnrod Éireann broke down on Wednesday night without a deal.
Discussions had been ongoing at the Workplace Relations Commission (WRC) over a pay increase for workers.
SIPTU is calling on Transport Minister Shane Ross to intervene.
Sector organiser Willie Noone said: "Critical talks at the Workplace Relations Commission aimed at diverting industrial action in Irish Rail broke down last night due to arrogant and incredible demands made by management.
"In return for a paltry 1.5% pay rise that would only become payable to workers next year management demanded that our members accepted outsourcing, forced redundancies, line closures and reduced contract hours.
"This was a derisory offer which management must have known would be totally unacceptable to our members. Irish Rail workers are in an unsustainable position where they have not had a pay rise but only pay cuts for the last decade."
He added: "SIPTU representatives are currently preparing for a ballot of our members in Irish Rail for industrial and strike action."
Unite has also confirmed plans to ballot its members for industrial action following the breakdown of talks.
Regional officer Willie Quigley described the company's 1.5% pay offer as "incredible" after an almost 10-year pay freeze.
Mr Quigley believes Minister Ross is presiding over a "public transport crisis not of the workers’ making".
"Iarnród Éireann workers will be unimpressed by the Minister’s call for the parties to return to the negotiating table, given Minister Ross’s failure to commit to a properly funded public transport system.
"The situation in Iarnród Éireann comes in the wake of disputes at Dublin Bus and Bus Éireann. The minister is presiding over a public transport crisis not of the workers’ making."
"We will be balloting in the coming weeks for industrial action at Iarnród Éireann up to and including strike action".
NBRU General-Secretary Dermot O'Leary said: "The National Transport Authority are on record as stating that Irish Rail has been underfunded by successive governments stretching back over a long number of years.
"The minister has a responsibility towards taxpayers, commuters and staff alike to ensure that the company is appropriately funded to meet its public service remit, inclusive of maintaining existing rail lines and paying those that work in Irish Rail a long overdue pay rise, similar to those awarded to others in the public transport space."