SIPTU has provided management at Tara Mines with proposals for cost savings and efficiencies, as an alternative to the company's plan to temporarily shut down the mine and lay of 650 staff.
The "comprehensive" document was put forward on the first day of "intensive talks" between unions and management.
Talks between both sides are due to reconvene in the morning.
In a joint statement following the meeting, the Unite and Connect unions said that management had failed to provide information on its current and future profits generated at the mine.
The statement said that the company had instead chosen to focus solely on its cost base.
Unite and Connect said that the Boliden Group, of which Tara Mines is a subsidiary, is an "exceptionally profitable company returning significant dividends to its shareholders".
They warned Boliden against "cutting costs on the backs of workers in Ireland".
Unite's Regional Officer Brian Hewitt said: "It is clear from both the parent group’s annual reports and the accounts of their Irish operations that Tara Mines is an integral part of the Boliden group, which has been consistently profitable over the past thirteen years.
"In the absence of evidence to the contrary, it appears to us that the decision to suspend operations at Tara was taken to reduce Boliden’s operating costs at a time when zinc prices are temporarily falling and demand can be met from inventory. Indeed, it is noteworthy that zinc prices rose by 3% following Boliden’s announcement regarding Tara."
Connect said that Boliden had failed to provide "any real financial justification for their decision".
They called on the company to immediately reverse its decision to suspend operations at Tara and also urged the Government "to make any assistance to the Tara Mines, as well as future licences, contingent on Boliden reversing its decision".
SIPTU said it would not make any further public statement until after tomorrow's meeting.
In a statement following today's meeting Boliden said it will give "due consideration to the proposals" presented by the unions.
"The situation that has emerged in relation to the company's finances is unsustainable and required urgent action to stem the cash outflow," the statement said.
"The decision to enter care and maintenance was taken so as to safeguard the long-term future of the mine."
Tara Mines is Europe's largest zinc mine and has been a major employer in the North East for almost 50 years.
Boliden said it made the decision to shut down to safeguard the long-term future of the company, in response to significant and unsustainable losses.
It listed a decline in the price of zinc, high energy costs and inflation as some of the reasons behind the decision.
Prior to today's meeting, SIPTU said it would enter the talks process with a "constructive attitude in an effort to ensure the future of this vital strategic economic asset" and "work towards an outcome which will maintain the operation of this mine".
Boliden said it would listen to the proposals unions put forward and "continue to converse with them as we have done over many years".
The company was not able to provide workers with a definitive answer on how long this period of "care and maintenance" would last.
The company reiterated the reasons behind its decision, saying that the situation that has emerged in relation to the company’s finances is "unsustainable" and that it had to take the decision to "stem the cash outflow".
Minister for Enterprise, Trade and Employment Simon Coveney met management and unions at Tara Mines last week.
Following those meetings, Mr Coveney said the company was in a serious and difficult financial situation.
He said he asked management to engage with the union "to make sure everybody is clearly in a position of understanding of where the company is financially".
