South Dublin County Council management and the IMPACT trade union have met at the Labour Relations Commission in a bid to avert a second one-day strike on 10 July.
The talks have adjourned until Tuesday, with sources saying some progress had been made but that it was slow.
The dispute centres on a decision by the council to withdraw "acting-up" and project allowances paid to staff for performing additional duties.
600 union members went on strike on 24 June, leading to the closure of a wide range of council services.
IMPACT has already warned that if the row is not resolved, it will mount a second strike next week.
Arriving for this morning's talks, IMPACT National Secretary Peter Nolan rejected suggestions that the union was breaching the industrial peace clause of the Haddington Road Agreement by going on strike.
He said it was management that had breached the HRA, which protects staff from further pay cuts or compulsory redundancies by terminating the payments without engaging in a process.
He said staff had already seen pay cuts of up to 25% and staffing reductions of 28%.
He said the parties had made some progress at a previous meeting, but described it as painfully slow.
He said he believed that they had the capacity to resolve this and prevent a dispute, but that if people chose to be obdurate, further industrial action would follow on 10 July.
South Dublin County Council representatives declined to comment.
The Department of Public Expenditure and Reform did not respond to queries as to whether the South Dublin County Council strike constituted a breach of the HRA.