There are 100,000 people on the social housing waiting list
The Simon Communities are warning that radical solutions are needed to address the ongoing housing crisis.
The homelessness charity was speaking after the Minister for Housing said significant progress is being made on the construction of new social homes.
New Government figures show just over 2,500 homes were completed by the end of 2017.
Authorities plan to build a further 3,800 social homes this year.
Housing Minister Eoghan Murphy has also set local authorities the target of completing 41,000 homes by the end of 2021.
Simon Communities spokesperson Niamh Randall said the country is still facing a crisis situation.
"Where there would be concerns really is about the pace of delivery," she said.
"These figures report 2,512 homes to be completed, under 4,000 homes which are under construction and about 2,000 homes which are ready to go on site.
"It is really important to note that this is in the context where we have got approximately 100,000 people on the social housing waiting list and massive pressures in the private rental sector."
She said more radical solutions are needed to cope with the scale of the situation.
"We have 10,000 people trapped in emergency accommodation," she said.
"Men, women and children living their lives trapped in emergency accommodation so clearly we need to look at mechanisms that can deliver homes really quickly.
"We are still waiting for the empty homes strategy, we need to look at rapid builds as well.
"We need to make sure that we get homes built and delivered really, really quickly."
Yesterday, Minister Murphy said he will seek increased funding for the Residential Tenancies Board in order to set the body up as an effective independent rental regulator.
The Rental Tenancies Act would make it a criminal offence for landlords to breach the 4% Rent Pressure Zone increase limit and force them to give longer notice periods to tenants before serving a notice to quit.
The new legislation also aims to introduce rent transparency by establishing a register to record rents paid at a property and make them publicly available.