Ten more prisoners have tested positive for Covid-19 in the Midlands Prison in Portlaoise, Co Laois.
It follows the completion of mass testing after three prisoners tested positive on Wednesday, and at least 11 staff have contracted the virus in recent weeks.
The Midlands Prison, which is the biggest jail in the country, has said a second round of mass testing will take place in the coming days.
A statement from the Irish Prisons Service (IPS) said it is continuing to work closely with the HSE and Public Health to contain the spread of the virus.
"The Irish Prison Service is continuing to work closely with HSE/Public Health and arrangements are being made with the HSE for the re-testing of all prisoners and staff, in order to provide an assured response to the current outbreak in Midlands Prison.
"This will support a return to a more normal prison regime as soon as possible," the ssatement said.
The IPS has also moved to reassure families of prisoners in custody that every step is being taken to ensure the safety of the inmates.
Prison staff will only contact the next of kin where a prisoner has contracted the coronavirus.
There are 824 prisoners at the Midlands Prison, when staff are included, more than 1,000 people will be tested in the mass screening taking place to contain the latest prison outbreak of Covid-19.