Behind-the-scenes moves to resolve the row which is causing widespread disruption to postal services began yesterday, but with no sign of a basis for formal talks.
The threat of a national strike, however, has been averted for the time being following a meeting yesterday of the executive of the Communications Workers' Union.
The union has had a mandate to implement a strike since last Friday, but decided to further defer a decision on when to begin the action.
By last night, 420 CWU members, employed at the Dublin Mail Centre in Clondalkin, had been suspended by An Post.
The company claims the union is engaged in industrial action at the centre by instructing staff not to carry out normal duties.
This is denied by the union, which claims the company has attempted to introduce new sorting arrangements without agreement.
The dispute has hit mail deliveries in Dublin as well as parts of Wicklow, Monaghan, Louth and Meath.
An Post is asking people not to post mail to or from Dublin city and county, Bray, Greystones, Wicklow, Carrickmacross, Castleblayney, Dundalk, Kells or Navan.
Mail for all of those areas is processed at the Dublin Mail Centre, which normally handles about three million items of post a day.
About a million items from the centre were delivered yesterday, as postmen and women have continued to work as normal.
A company spokesman, however, said fewer deliveries would take place today as the service began to wind down as a result of the suspensions.
Customers are also being advised not to post to or from Tuam, Co Galway and Drogheda, Co Louth, where deliveries have been disrupted for almost two months because of separate disputes.
The Labour Relations Commission (LRC) made informal contact with both the union and management yesterday with a view to finding a basis for talks. The sides are so far apart at present, however, that formal discussions are considered unlikely to begin until later in the week.
Mr Seán McDonagh, of the CWU, said the union was available for talks in any forum, while a company spokesman said it would consider any approach.
The Minister for Communications, Mr Dermot Ahern, was urged to intervene in the dispute.
Mr Tommy Broughan TD, the Labour Party spokesman on communications, said ultimate responsibility for the situation at An Post rested with the Minister.
"He cannot stand by and let the situation deteriorate as the public takes the pain of severe postal disruption. I am appealing to him to intervene immediately or appoint an independent mediator to settle the dispute."
Mr Ahern, however, said he was continuing to be briefed on the dispute and he understood the national implementation body (NIB), an ad-hoc social partnership group sometimes called in to deal with disputes, was meeting yesterday.
It is understood, however, that there are no immediate plans to involve the NIB and attempts at a resolution are more likely to rest with the LRC.
An Post began suspending staff at the mail centre late on Friday night after they began refusing to carry out management instructions.
An Post says staff have been using machinery at the centre, by agreement, for the past year as part of their normal work. Mr McDonagh, however, said staff had been engaged only in testing the machinery and in training, pending an agreement on its use.