The Department of Justice has said that together with the HSE it will "pilot an off-site self-isolation facility" for asylum seekers suspected of having Covid-19, who are living in Direct Provision or emergency accommodation centres.
Two asylum seekers are reported to have tested positive for Covid-19 in two separate direct provision centres.
The Movement of Asylum Seekers in Ireland said it learned of one case yesterday.
While the Irish Refugee Council has said that it is aware of a case in a different part of the country.
MASI has criticised what it has called an inconsistency in the implementation of measures to curtail Covid-19 across the countries 72 direct provision centres and emergency accommodation providers.
It has launched a petition calling for those aged 60 years and over, and those with pre-existing medical conditions, to be relocated to places where they can self-isolate, subject to their informed consent.
It said that with tourist numbers "in decline due to the current situation, there will be capacity in various places in the State."
The CEO of the Irish Refugee Council has also written to the Minister for Justice requesting that "the Government consider moving people, who are within the HSE risk categories, to accommodation where they can adhere to social distancing... and self-isolate and cocoon if necessary."
In a statement, the Department of Justice said a dedicated team has been established in the International Protection Accommodation Service to manage issues relating to Covid-19 in all accommodation centres.
The off-site self-isolation facility to be piloted with the HSE will be for residents suspected of having the virus, or those who have tested positive and who have mild symptoms.
All accommodation centres have been asked to complete contingency plans for Covid-19.
The Department also said that each centre has been asked to generate "a self-isolation capability."
In addition, it said the HSE was currently considering the most effective "prevention and cocoon measures" for the most vulnerable residents in centres.
To support social distancing, it added that no isitors were allowed and that centres without independent living arrangements have been asked to implement staggered meal times or to provide takeaway facilities where canteens have been temporarily closed.