The Irish Postmasters' Union claims up to 400 post offices are in danger of closing in 18 months' time.
It is after more than 160 post offices closed last year.
Ned O'Hara, from the IPU, says the entire network will soon be in jeopardy unless the new government gives it more support.
"The people who signed the new contract are currently getting support payments for the next 18 months.
"The busiest Post Offices are under threat. It's not just the small rural Post Offices that are under threat, it's the busy urban offices," he added.
If those big urban offices go out of business the entire Post Office model is broken.
Almost nine-out-of-ten people say they want to see Government financial support to keep their post offices open.
Some 86% of people also said they want more State services processed in local post offices, according to a new survey carried out by Red C.
Some 1,015 adults were surveyed on the future of the post office network amid fears that the removal of some services from the network could result in mass closures in the coming years.
Some 91% said their post office provides a valuable service to the local community, while 86% support the Government providing financial support to keep their post office open.
Support was strongest among older people and outside of Dublin, though more than 80% of young people also said they want action to maintain their post office.
Meanwhile, the price of stamps will increase on March 19.
The cost of a standard domestic stamp will rise from €1 to €1.10.
Meanwhile, the cost of a standard international stamp will increase from €1.70 to €1.80.
An Post says the increases reflect other price-rises throughout Europe.