An Post says mail deliveries should be back to normal by Monday following the disruption caused by the 24-hour stoppage by workers on Wednesday.
A spokesman said yesterday that a backlog of 3.5 million items of mail remained in the system after large volumes were posted on Thursday.
However, special arrangements had been put in place for the weekend to ensure the backlog would be cleared by Monday.
The Communications Workers' Union (CWU), which organised the stoppage on Wednesday, says there will be no further disruption to mail deliveries before Christmas.
Members of the union have finished balloting on restructuring proposals, including job cuts and overtime cutbacks in the company's collection and delivery service.
A result of the ballot had been expected yesterday, but the union decided to delay an announcement until next week. If members reject the proposals, as expected, they are likely to be referred to the Labour Court for adjudication next year.
The union and the board of An Post are to hold separate meetings next week with the Minister for Communications, Mr Dempsey.