There are calls for the ban on rent increases and evictions to be immediately extended.
Threshold says the moratorium introduced by the government is due to expire on June 27.
However, it says rents increased throughout the country before the pandemic began.
It also believes people living in the private rented market are at great risk of poverty and social exclusion.
The moratorium on evictions and rent increases came into effect on March 19 after being introduced for the duration of the emergency to ensure people can stay in their homes during the crisis.
The notice period for tenancies of less than six months was increased from 28 to 90 days in last month's announcement by Social Protection Minister Regina Doherty.