Fine Gael has called on both sides in the postal dispute to return to the Labour Relations Commision (LRC) "with an open mind".
The LRC is expected to renew contact with An Post and the Communications Workers' Union (CWU) today after separate talks on Wednesday were unable to find a basis for discussions.
Speaking on RTÉ radio this morning, Mr Simon Coveney of Fine Gael said Mr Ahern "needs to insist that management, who are there working on behalf of him as shareholder, go back with an open mind to the LRC. And I think the union leaders in ICTU also must insist that the CWU also go back to the LRC with an open mind."
The dispute is now in its seventh day with little or no postal deliveries in Dublin and other areas across the State.
The dispute began at the weekend when An Post began suspending staff at its Dublin Mail Centre in Clondalkin for refusing to carry out management instructions. The CWU has accused management of trying to cripple the debt-ridden company.
By yesterday, 553 employees had been taken off the payroll at the centre, in addition to 89 casual staff in delivery offices whose contracts were suspended because the company had no work for them.
The Minister for Communications, Mr Dermot Ahern, yesterday urged the company and the CWU to maintain contact with the Labour Relations Commission.
An Post is asking customers not to post to or from Dublin city and county, Bray, Carrickmacross, Castleblayney, Drogheda, Dundalk, Kells, Greystones, Navan, Tuam and Wicklow.
Postboxes in Drogheda have been sealed for a number of weeks because of an unofficial dispute concerning overtime. On Wednesday, An Post began sealing postboxes in other affected areas.