Further strike action due this week, with a four-hour stoppage planned for Thursday, and a day of strike action on Friday
SIPTU and Luas operator Transdev are being urged to re-engage in negotiations to resolve the long-running row over drivers' pay.
Labour TD Joan Burton, who recently stepped down as party leader, believes says talking and using the Labour Court's mechanisms is the best way to resolve the dispute.
On Friday, tram drivers represented by Siptu staged a 12th day of industrial action over their demands for higher wages.
Further strike action is due to take place next week, with a four-hour stoppage planned for Thursday, and a full-day strike on Friday.
Transdev says it will deduct a full day's pay from drivers who take part in four-hour work stoppages.
Drivers are seeking increases of about 23 per cent over the next three years. Transdev has said it will offer no more than the 13 per cent over three years accepted by other grades of employees in the company.
The Luas operator has faced fines of up to €100,000 a day for failing to provide a Luas service on the days of strike.
Labour TD Joan Burton, says all sides must endeavour to end the industrial dispute as quickly as possible.
"I certainly hope that a resolution will be found for that as soon as possible.
"And the only way that that can really be done is talk between the parties. That's the only way, to me, of actually doing it."