An Post says the situation at the company remains very serious and that their advice to the public not to post mail remains in place.
It says it is making this statement with great regret and has called on all the parties involved to use the channels available to resolve the dispute.
It says Post Offices will open tomorrow and post that is in the system will be delivered.
In response to union suggestions that much of the mail could be processed without the machinery, it says that 80% of mail goes through an automated system and the impact of the action is such that the company cannot take in mail.
Concern has been growing and contingency plans are being put in place as there appears to be no breakthrough in the dispute which has resulted in the suspension of the postal service.
The concerns come as the Communication Workers Union has warned An Post that if it issues protective notices to postal workers it will ballot for industrial action.
A group representing older people has called an An Post to clarify how long the suspension of postal services is likely to continue.
Active Retirement Ireland said it is worried about the uncertainty around the instructions issued by An Post to the public last week not to post items until further notice.
Spokesman Peter Kavanagh said the suspension of services disproportionately effects older people, particularly those in isolated rural areas and those with no experience of, or access to, broadband and computers.
He said these people, who are among An Post's most loyal customers, need certainty as to when the situation will be resolved so that they can get back to their everyday business.
The Department of Social Protection says contingency plans are in place for the thousands of social welfare cheques that are due to be issued tomorrow.
It says details of how the cheques will be sent to clients has not yet been finalised.
However, RTÉ News understands that they may be made available for collection at social welfare offices.
Child Benefit is due to be paid to parents on Tuesday, but the Department says the majority of these payments are made electronically.
The Department has also advised those who are intending to apply for the €100 Water Conservation Grant to do so online before the deadline of 8 October.
It says applications cannot be made by post and that the Department is giving phone assistance to those who need help making their applications electronically.
The Department of the Environment, who look after the issuing of Motor Tax discs, says it is continuing to monitor the situation in relation to postal applications for the service.
Electric Ireland says its keeping the situation under review and although many customers use online billing they will make arrangements to accommodate those who do not as appropriate.
The Office of the Revenue Commissioners has said their website contains extensive information to assist customers to understand and comply with their tax obligations in light of the postal issues.
CWU may ballot for industrial action
In a letter to An Post, the CWU's National Officer, Sean McDonagh, said issuing protective notice would be a "serious escalation" and "wholly unjustified"
The union has also queried what its describes as An Post's "bizarre" decision to suspend the postal service when its says many items are not sorted by the machinery at the centre of the dispute.
It says parcels, periodicals, registered items and passport express items are currently sorted manually.
The union said manual sorting could be extended to other services and that the union would co-operate with this.
It said in these circumstances it is astonishing and ridiculous that staff in the four sorting centres were sent home early.
CWU General Secretary Steve Fitzpatrick accused An Post of shutting down mail operations to bolster the position of IO Systems in their industrial relations dispute.