Michelle Norris also warned against the Government allowing home and apartment standards to be lowered in order to help developers build.
In an interview with the Irish Examiner, Ms Norris outlined the work of the State agency and how significantly more social housing building is needed to help resolve the housing crisis.
The agency, mainly borrowing from EU banks, has a loanbook of some €3.6bn which it primarily lends to housing agencies at low rates for the building of social housing.
An estimated 100,000 people are waiting for homes on the social housing list.
Any attemp to resolve the crisis must first address social housing, said Ms Norris.
“I think we have very significant challenges in relation to providing social housing,” she said. “We have some very significant short-term challenges because there are very large numbers of households in homeless accommodation, particularly in cities.
“Lower-income houses are having enormous trouble securing private rental accommodation with state subsides like rent supplement. Those subsides have become very difficult to operate particularly in cities. So we have an immediate problem in trying to accommodate these households, particularly those in homelessness.
“It is very difficult to see how that will be solved without increasing our rate of social house building very rapidly in the near future.”
One way to boost the levels of social housing provision is to allow local authorities the funds to build them, said Ms Norris.
“I can’t see how we will solve the housing crisis without local authorities getting large scale delivery of social housing,” she said.
“I think local authorities should be given access to the Housing Finance Agency to borrow for housebuilding. It needn’t necessarily accrue permanently on the local authority balance sheet.”
The Government is preparing to launch an affordable housing initiative in the coming weeks.
Previous schemes, in Dublin, stopped after the crash and many buyers now cannot afford to buy.
A recent scheme in Ballymun, Dublin, saw two-bed homes being sold for €140,000, drawing praise from Housing Minister Eoghan Murphy.
However, Ms Norris said arrears on affordable local authority schemes dating back years are running at 31%, with borrowers unable to afford repayments.
The Housing Finance Agency has taken over the underwriting of these loans and arrears.
Ms Norris said: “We need to be careful not to repeat the mistakes of the past. I think we need to be careful introducing supports for low-income home buyers that are actually affordable. And we need to ensure we don’t end up in a situation where people are in arrears on a mortgage for an affordable home.”
She also warned that, in Dublin and Cork, social or affordable homes are being sold on at huge profits. Instead, the homes should always be costed and, if sold, remain affordable for future owners.
“It means the taxpayer pays the cost of providing the housing and the profits are privatised,” said Ms Norris.