The Irish Postmasters Union has vowed to continue its industrial action at 600 sub-post offices throughout Ireland.
IPU members who operate rural post offices are currently refusing to accept deliveries before 8am as part of a dispute over pay.
The action, which began last week, has caused minor disruption and delays and the IPU has vowed to escalate it if An Post refuses to enter negotiations.
Spokesman John Kane said: "It was a measured response on our part to management’s failure to deal with legitimate grievances on behalf of our members.
"We believe that as the days roll on, the action will in fact escalate to the point where management will find that the whole mail is going to be unmanageable."