Attempts to resolve the dispute at Brinks Allied, which has disrupted deliveries of cash to ATMs in Dublin and the east coast, will continue today with a hearing at the Labour Court.
The dispute was referred to the court yesterday after talks at the Labour Relations Commission failed to produce a resolution.
Workers at the company plan to go on strike from Thursday if the row, over an attempt by management to introduce new security procedures, is not settled.
The action would increase the threat of ATMs in the affected areas being left without cash, as supervisors currently carrying out deliveries would not pass strikers' pickets.
However, banks say they are confident that even in the event of a strike, most machines would continue to operate normally.
Ms Jennifer Chamberlaine of the Irish Payment Services Organisation, which represents the banking sector, said that between 90 and 93 per cent of ATMs in the areas affected by the dispute were functioning yesterday.
The banks were "working extremely hard" to maintain cash supplies and there was no reason why the current level of service could not be maintained, she said.
The IPSO recognised that there were some blackspots, mainly high-traffic areas where demand for cash was strong, and was continuing to encourage the use of alternatives such as laser and credit cards.
Today's hearing will be the first involvement of the Labour Court in the dispute, after the failure of several attempts at conciliation.
In a statement yesterday, the LRC said that in view of the differing views of management and the union involved, SIPTU, it was proposing the referral of a number of matters to the court for investigation and recommendation.
The dispute began on July 30th when Brinks attempted to introduce new vehicles and work practices, which workers claimed would leave them more vulnerable during armed robberies. Staff have not been carrying out deliveries since then, although they say they remain available to resume "normal working".