The Minister for Communications, Mr Demspey, has called the parties in the postal dispute together as the Communications Workers' Union (CWU) warned today's 24-hour strike will escalate.
More than 2,500 workers stopped outside the GPO on their way to protest outside Leinster House with banners calling for An Post chief executive Mr Donal Curtin to "pay us our money now".
Wage rises due under Sustaining Progress to staff and pensioners have not been paid since November last year. The company says it is facing massive losses and cannot afford the increases.
Mr Dempsey this evening urged workers not engage in further action and has invited An Post directors and union officials to talks later this week but said resolution can only be achieved through the industrial relations machinery of the State.
"It is absolutely vital that agreement is reached in the shortest timescale possible to allow An Post to survive," Mr Dempsey said.
The CWU executive meets tomorrow to decide on the union's next step and a spokesman warned this evening that the action will escalate if the union's demands are not met.
The unions is also unhappy at the company's plan to lay-off workers at its Special Delivery Service (SDS) and reintegrate the company as part of a general restructuring of An Post
Members of the Civil and Public and Services Union (CPSU) at An Post came out in support of their colleagues today.
The CPSU represents clerical workers primarily in the financial services division of An Post and is the second largest union in the company.
Speaking at the CWU rally outside the Dáil, the union's general officer Mr Eoin Ronayne said the union's members were also concerned about their future.
"I can say we are very worried - we have been shown little respect by management despite having delivered the savings and cuts asked for," he said. "Where is the honour we have a right to expect from management in this era of so-called partnership?"
Around 30,000 social welfare payments will be delayed because of the action which could disrupt mail deliveries well into the weekend.
A spokeswoman for An Post said the strike was unnecessary and in clear breach of procedures.
"The CWU is ignoring agreed industrial relations procedures by taking unofficial industrial action which will accelerate the undermining of public confidence in the mail system," she said.
An Post added the action would deliver a further damaging blow to a business which is in decline and had an operational loss of €43 million last year.
The company said 1,350 sub-post offices throughout the State will be open tomorrow. Many of these handle social welfare payments.