SIPTU have said the Luas could be facing "sustained, on-going industrial action" unless agreement is reached over pay claims.
Members have announced two additional 24-hour work stoppages in their dispute over pay and conditions.
It will see no services run on Tuesday March 8th and Thursday March 17th, St Patrick's Day.
Transport Minister Paschal Donohoe said the announcement of further strike action is "extremely disappointing".
"News that Luas workers are to stage a further two days strike action on the 8th March and again on St Patrick's Day will come as exceptionally bad news not only to commuters, who rely on Luas for their daily commute, but also to the 100,000 overseas visitors who will travel to Dublin to help us celebrate our national holiday".
"Commuters were seriously inconvenienced last week when a 48 hour strike was held. It appears the decision to stage a further two days of strike action, in particular on St Patrick's Day, is being taken with a view to causing maximum disruption, which will be welcomed by no-one", he added.
SIPTU transport organiser, Owen Reidy, told Newstalk Breakfast: "Unless the employer can come to the table with new thinking, I think we're in for a period of sustained, on-going industrial action".
While Transdev managing director, Gerry Madden, added: "The irony here is...at the end of the day, every time there's a strike our financial position worsens and it decreases our ability to make a pay award to our people".
Asked how they could settle this dispute, Mr Madden said: "I have an old-fashioned view - it might not necessarily be described as a bright idea or rocket science - but getting into a room and having meaningful conversation would sound like a good idea to me".
"I don't see this as an intervention that needs to be made by the government...and it should not be down to the taxpayer to meet demands of €30m", Mr Madden added.
While Mr Reidy commented: "The one thing I do agree with Gerry on - but he needs to start to do it, rather than repeat rhetoric - is we need to get into a process where management need to have a flexible and new approach and reach an agreement with us".
