The Minister for Communications, Mr Ahern, has rejected a call by the Fine Gael leader, Mr Enda Kenny, for him to intervene in the postal dispute.
As ballot papers were distributed to members of the Irish Postmasters' Union (IPU), Mr Kenny claimed it was "way beyond time" for the Minister to attempt to broker a settlement.
A spokesman for the Minister, however, said the dispute would ultimately have to be resolved between the parties concerned.
More than 1,700 sub-post offices are to be closed for all services except social welfare payments from Monday, December 2nd, if the dispute over pay is not resolved.
That would leave fewer than 100 post offices, those that are run directly by An Post, open in the run-up to Christmas. Mail deliveries could also be delayed.
The dispute left thousands of homes and businesses in east Mayo without postal deliveries yesterday, after postmasters picketed the main post office in Claremorris.
The action by 18 members of the IPU began at 2.30 a.m., and no mail trucks passed the protest while the unofficial picket was in place.
A spokesman for An Post, Mr John Foley, described the action as "over the top". As a result, there were no deliveries yesterday in a large area of the county.
The towns affected included Claremorris, Swinford, Kiltimagh and Charlestown. Rural areas surrounding them were also left without post.
The postmistress of Kiltimagh post office, Ms Marian Dunne, who took part in the picket, said the protesters had acted because of frustration over the refusal of An Post to make any reasonable offer.
"We are out here in the gale-force winds and rain in an effort to make our voices heard," she said.
"We will be voting on an escalation of the industrial action when we receive our ballot papers, and it is clear from the mood here on the protest line this morning that there will be resounding support for further action. Our protest will not be confined to a single day", she said.
IPU members began their industrial action in August by refusing to open their premises before 8 a.m. They are seeking improved pay for early-morning work and other functions.