The NBRU is calling on Transport Minister Shane Ross to establish a forum for talks
The Bus Éireann strike is entering its fourth successive day, with no end in sight to the dispute over cost-cutting plans.
Members attached to several unions at the embattled company began an all-out strike on Friday.
A majority of Bus Éireann services are not operating, although School Transport is not expected to be affected.
The company has insisted that it faces insolvency within months if it does not introduce a wide range of cost-saving measures.
However, unions have refused to agree to changes to workers' pay & conditions.
Last night, the National Bus & Rail Union (NBRU) called on Transport Minister Shane Ross to establish a forum for talks.
General Secretary Dermot O'Leary said: “We are calling on the Minister to provide the kind of leadership that is vital towards resolving this dispute.
“It is inconceivable that Management can continue to wreck the national transport system by continuing to insist on a race to the bottom to establish a yellow pack bus company when a solution to the current Expressway crisis could be arrived at through talks centred on the already mooted efficiency based agenda," he added.
Many trains were cancelled last week when drivers refused to cross pickets at the stations they share with Bus Éireann.
Irish Rail is assuring passengers that all services are operating on all routes today.
Management has stressed they are not part of the strike and do not expect disruption today.
However they also note that Bus Éireann tickets are not valid on train services, and higher demand is expected as a result of the bus strike.