Almost 200 inmates are currently sleeping on prison floors because of overcrowding issues.
In a statement, the Irish Prison Service (IPS) said it has no control over the number of prisoners sent to it by the courts.
There are currently 4,583 prisoners in the country’s jails.
It means the country’s prisons are just over capacity at 104%.
Mountjoy meanwhile is operating at 110%.
Some 194 prisoners are sleeping on mattresses on the floor – which is four times the amount seen at the start of the year.
The situation is leading to concerns for the safety of both prisoners and staff.
The IPS said it has to accept all prisoners sent to it by the courts and it has no control over the number of inmates committed to custody.
It said the prison system is subject to peaks and troughs and it is working with the Justice Department to ensure a safe environment.