They were due to be completed by June, he said.
The increase in demand was due in part to a culture change which meant people knew they would receive the help they need, he said.
Faafoi added that Budget 2019 had included $197 million to strengthen and expand the Housing First programme.
That funding would be able to support up to 2700 homeless whānau across New Zealand, he said.
However, National's Associate Housing spokesperson Simon O'Connor said: "Labour was too quick to meddle in the rental market when it should have been focused on building houses.
"The reason we're in this mess today is because KiwiBuild tanked, Labour's new rental standards scared off landlords at the affordable end of the market, and its decision to end tenancy reviews increased pressure on social housing supply."
If National were to get back into government at this year's election, it said it would "prioritise our most vulnerable Kiwis by throwing our weight behind community housing providers and introducing a target to reduce the time it takes MSD to house Priority-A clients on the social housing register".
Faafoi said every New Zealander had a "right to a warm, dry, secure and safe place to live".
"Homelessness is a complex and growing problem that will take a concerted and sustained effort by multiple agencies to ensure homelessness is both brief and non-recurring."
Demand by region
Northland: 524
Auckland: 5326
Waikato: 1494
Bay of Plenty: 1120
East Coast: 1405
Central: 803
Taranaki: 255
Wellington: 1595
West Coast Tasman: 510
Canterbury: 1063
Southern: 380
Other/unknown: 21
- RNZ