More than 220 new prison spaces will be opened by the end of the year to alleviate the worsening problem of overcrowding in the jails, according to the Minister for Justice Helen McEntee.
The Prison Officers Association said the problem has led to increased levels of tension and violence in the prison system.
The POA told the minister that 600 new prison spaces are needed.
Ms McEntee also accepted that there were not enough prison officers and was hoping to address the issue of additional recruitment in the forthcoming budget.
Earlier, the POA said while more courts have been opened all over the country and more people are being sent to prison, the corresponding necessary resources to keep them safely in custody are not being allocated.
Prison officers also called for the reopening of a training unit at the Mountjoy complex in Dublin.
Violence in prisons, overcrowding, pay and the problems with controlling and restraining difficult inmates are among the issues of concern for prison officers.
Officers say 35 inmates slept on mattresses on floors in Cloverhill Prison one night this week, almost 10% of the prison population, with four being placed in three person cells.
The POA said overcrowding is also becoming an issue in Cork Prison and Dochas Women's Centre in Dublin, and is leading to increased levels of tension and violence.
The problems, they say, are being caused by the opening of additional courts in Croke Park in Dublin, in Drogheda, Mullingar and in Castlebar, which is leading to more people being sent to jail without the necessary additional resources being allocated to the prisons.
Assistant General Secretary Gabriel Keaveny said these must be allocated immediately, and that the training unit at Mountjoy in Dublin should be reopened to accommodate inmates.
The association also said it wants the regulations for controlling and restraining violent inmates placed on a legal footing to protect officers who abide by them.
Mr Keaveny said an officer who abided by the manual was subsequently charged with assault and although acquitted in court, the POA said the judge found the regulations had no basis in law.
He warned that if prison officers are not legally protected, they will refuse to operate the control and restraint manual, and in future call gardaí into the prisons to deal with violent inmates.
The POA also called on the Taoiseach to correct the Dáil record after he made what they described as "outlandish contributions" in relation to allegations of misconduct by prison officers which were subsequently found not to have occurred.
POA General Secretary John Clinton said the issues were fully investigated, the allegations were false and added that the association wrote to Micheál Martin twice but had not received a satisfactory response
"We would like the Taoiseach to correct his contributions made to the Dáil, and clearly point out that there was no misconduct whatsoever on behalf of our members working on that evening in Cloverhill Prison," Mr Clinton said.
Ms McEntee said the issue was a matter for the Taoiseach.
His office said Mr Martin looks forward to reading the report on the matter which will be published shortly.
In relation to the Kinahan organised crime group, the minister said the 79 gang members in prison here were being managed effectively and very well to date.
She also said authorities were liaising with their counterparts in the United Arab Emirates in relation to the leadership of the gang.
Ms McEntee added the seizing of its assets there precludes the Kinahans from carrying out their day-to-day business, which she said "is obviously what we want".
