Efforts to resolve the dispute at Brinks Allied have resumed with both sides taking part in talks at the Labour Court.
Yesterday the issue was referred to the court after the failure of discussions at the Labour Relations Commission.
Siptu Security Services Branch Secretary Mr Kevin McMahon said he was looking forward to the Labour Court "impartially investigating the issues and making a recommendation that can resolve the dispute".
The dispute has affected deliveries of cash to ATMs in Dublin and the east coast. It centres on new security procedures introduced following a sharp rise in the number of robberies on cash delivery vans. The issue is now in its third week.
Staff at the firm have voted for strike action on Thursday if the dispute is not resolved.
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.