The Irish Penal Reform Trust (IPRT) is calling for the resumption of physical prison visits as a matter of priority.
Visits were suspended on March 27 to help stop the spread of Covid-19.
Justice Minister Charlie Flanagan has confirmed they will resume, but has not yet put a timetable on this process.
While five prison staff were reported to have contracted the virus, it did not make its way into the prisoner population.
Mr Flanagan said he is "acutely aware of the supportive role" played by friends and families in the "rehabilitation of prisoners and in their preparation for life in the community after release from prison".
Despite this, Mr Flanagan said "the risk continues and must be managed".
"The Director General has assured me that the Irish Prison Service is committed to reintroducing physical visits as soon as it is safe to do so," Mr Flanagan said.
"The Irish Prison Service has started a detailed assessment of the ability of each prison, within its physical and resources confines, to resume some family visits, with appropriate safeguards in place having regard to the need for infection control.
"While no date has yet been identified and the safety arrangements that will be put in place have yet to be finalised, the Irish Prison Service will provide further information and a date for the gradual recommencement of visits to prisoners and their families in the coming weeks."
IPRT said it is important that restrictions are "safely eased in line with public health advice and in line with the easing of measures in place in other residential settings".
The group said: "Decisions on the reinstatement of visits — particularly children's visits — must be continuously guided by public health advice rather than security concerns."
"While the Irish Prison Service’s response to Covid-19 has been successful in keeping prisoners Covid-19-free, it now has the opportunity to extend its use of best practice to the easing of restrictions across the prison estate.
"While many of the measures introduced by the Department of Justice and Equality and the Irish Prison Service in response to Covid-19 were proportionate to the risk posed, IPRT, led by international human rights guidance, believes that these restrictions should be in place for the shortest possible timeframe."
During the suspension of physical visits, a number of "new innovations" including video calls were introduced.
Mr Flanagan hopes to continue these even after the reintroduction of physical visits.