SIPTU President Jack O'Connor has said he is ready to engage with anyone on the Luas dispute but management must improve their offer.
Acting Minister for Transport Paschal Donohoe said earlier that the Luas strikes are "not acceptable" and he will not take out the taxpayers' cheque book to solve the pay dispute.
Luas employees overwhelmingly rejected pay proposals that included pay increases of up to 18% over a period less than three years.
Planned strike action on Easter Sunday and Easter Monday will affect thousands of people planning on visiting the 1916 Centenary commemorations in the city centre.
Speaking on RTÉ’s Today with Sean O’Rourke, Mr O'Connor said: "There is ample time for an engagement to take place with a view to addressing the inadequacies in the proposal that was put that would enable the dispute to be called off."
There are 48 hours available before the planned strikes to address "considerable inadequacies" in the proposal, he said.
"The proposal itself contains a very, very regressive concept, which is the idea that the people who are recruited between now and when the Luas extension is ready to go, that they would be paid on a new entry lower rate - which is considerably lower than the lowest rate which applies to workers when they join the company at the moment and this is a concept which has been objected to strenuously.
"We are ready to engage this minute, but we have no one to engage with," Mr O'Connor added, "it’s not in my hands."
He said: "We will not be issuing any knee-jerk response. This decision has serious implications for the company and our staff and we will reflect over the weekend and issue a considered response."
Mr O'Connor also insisted the offer made to drivers had been misrepresented and amounted to 10% over three years.
Luas operator Transdev has disputed this assertion and said 58% of drivers would be up 18% by January 2019, not including the bonus.
Luas strike 'not acceptable' - Donohoe
Speaking on RTÉ's Morning Ireland, Minister Donohoe said: "I'm not going to take out the cheque book of the taxpayer here to resolve an issue and in so doing create massive costs for the taxpayer in the future and undermine our ability to resolve issues like this across our entire economy.
"As Minister for Transport, it’s not acceptable to me that a form of public transport now faces indefinite strikes into the future," he said.
After four days of strike action in February, and the threat of further action on St Patrick's Day and Easter, Luas operator Transdev and SIPTU hammered out proposals at the Workplace Relations Commission (WRC) in a bid to resolve the dispute.
Of the 167 drivers who voted, only two voted in favour of the WRC proposals.
"I believe it is now vital that the leadership of SIPTU engage in this matter to ensure the strikes that are planned for Easter Sunday and Easter Monday do not happen," Mr Donohoe said.
He added that members of the public who have heard some of the figures in relation to this wage agreement will note that "they are significantly ahead of the expectations that they have regarding their own salary in the future – and they are massively ahead of the ability of, for example, CIE or any public transport organisation to pay for.
"This is an agreement that Transdev felt they could negotiate and pay...and the fact that it was defeated by such an overwhelming number of votes is intensely serious for how the Luas will be delivered in future," the minister said.
Management at Transdev expressed their "shock and disappointment" at the rejection of the proposals.
Managing Director Gerry Madden said the proposal was at the "very outer limits of what we could afford" and in "accordance with the terms of the WRC document that proposal is now withdrawn".
SIPTU Divisional Organiser Owen Reidy said: "It seems quite clear that there is a complete breakdown in the relationship and trust between the driver grade and management at the company.”
He said some drivers rejected the proposals because "drivers did not want to accept a new pay scale that leaves new entrants on lower pay than current staff".
With regard to private bus operators and local transport arrangements during the planned Luas strikes, the Coach Tourism and Transport Council of Ireland has said the dispute is a matter between the company and its employees.
It added that "CTTC members will continue to provide transport to the travelling public who have been seriously inconvenienced by this dispute through the provision of scheduled services under licence from the NTA".