An Post has indicated that 265 post offices around the country are unviable and may face closure.
Speaking on RTÉ's Prime Time
last night the Chief Executive of An Post, David McRedmond, said if the company do not "make the changes that are needed for the future ... then the whole system will collapse."
Mr McRedmond said the company have identified 265 post offices that are "near no discernible area of population."
He said the "target for the Department of Social Protection is that everybody be within 15km of a post office," adding that at present "70% of the population are within 15km of five post offices."
However, speaking on the same programme the Minister for Communications called for modernisation to bring revenue into struggling post offices.
Denis Naughten said they "can bring additional revenue into the post offices and make many of those post offices that are currently struggling viable by using technology rather than seeing it as the demise of the post office
Earlier yesterday more than 50 members of the Irish Postmasters' Union held a protest outside the Taoiseach's constituency office in Castlebar, Co Mayo.
They called on Enda Kenny to show leadership in securing the future of the postal service.
There are currently 1,100 post offices in operation around the country and it is estimated there could be in the region of 600 closures under An Post's restructuring plan.
Workers say they will resist any such moves by An Post.
Most of the postmasters who took part in the protest are from rural post offices across Co Mayo.
They vented their anger on the Taoiseach's doorstep and handed in a letter calling for his resignation if decisive action is not taken to protect and support the service.
An Post is close to finalising its restructuring plan and Minister for Communications Denis Naughten says he wants to deliver a sustainable postal network across the country.
He said the focus would be on new digital opportunities, while working closely with management and staff of An Post.
Postmasters gathered in Castlebar say that post offices are the lifeblood of local communities and that their closure would be detrimental to rural Ireland.
The IPU says the Government has failed to sanction additional services such as motor tax, the updating of the electoral register and educational and health service payments to secure a future for the local post office.
In the letter handed into Mr Kenny's constituency office, the union called on Mr Kenny to implement a strategic plan immediately in order to secure a viable future for the post office network.