Members of the National Bus and Rail Union (NBRU) are to meet for exploratory talks on Dublin Bus.
The NBRU say they have agreed to attend the Workplace Relations Commission (WRC) for the talks on Monday.
General Secretary Dermot O'Leary said: "Whilst the request to attend at talks without preconditions is something the trade unions have long been calling for, the fact is that our members are extremely angry that the inaction to-date by the company and the Department of Transport has caused severe disruption to commuters and staff alike.
"The NBRU focus from the commencement of this dispute has been geared towards getting Dublin Bus to attend at discussions in order to address the fact that its own staff are deserving of a fair and adequate wage rise after eight long years of austerity enforced pay stagnation and pay cuts.
"Any decision we have to take in relation to postponing our member’s industrial action is one which we will only consider after first establishing if Dublin Bus are serious about engaging in comprehensive discussions towards a resolution of this dispute on behalf of the 400,000 commuters and 3,500 staff".
SIPTU have also accepted an invitation to attend the talks. SIPTU Transport Division Organiser, Owen Reidy, said: “We understand that the purpose of this initial meeting is to see whether there is the basis for a meaningful negotiation between the parties. Any decision as to whether the pending strike action by our members on Tuesday and Wednesday of this week goes ahead, or is cancelled, will be made by the union committee based on the progress, or otherwise, at tomorrow's initial meeting.”
Thousands of commuters and businesses faced severe disruption across the weekend, as workers went on strike for a fifth and sixth day.
Retail Excellence Ireland (REI) claims retail sales plunged by up to 60% on Saturday and Sunday.
Drivers at the company are in a long-running row with management over pay, with 13 more strike days scheduled for this month and next.
It says that, to date, the industrial action has cost the company in excess of €4m "and continues to impact the financial stability of the company."
Further stoppages are due next month on the 1st, 5th, 7th 10th, 12th, 14th, 18th, 19th, 24th, 26th and 29th of October.
Union members are seeking a 15% pay rise over the next three years, as well as a payment in lieu of an agreed 6% increase that was deferred in 2009.
