Dr Smith said it would be challenging to construct the new houses at an affordable rate, but he was confident it could be done.
The three new sites, along with a previously announced 200-house development in Moire Rd, Massey, cost $52 million and further funding for the scheme is expected in Thursday's Budget.
Labour Party housing spokesman Phil Twyford said the Government had under-delivered.
When announcing the policy a year ago, it said it owned 500ha, which had the potential for 10,000 homes, he said.
"Having spent $50 million to only secure development agreements for 13ha is a flop," Mr Twyford said.
Dr Smith stood by the long-term target of 10,000 homes, but said reaching it would require further capital injections. "Those numbers are still achievable," he said.
Agreements with developers were expected to be signed off between August and the end of the year for the new sites, and the first dwellings were expected to be built within 18 months.
The sites that featured apartments were likely to take up to two years.
"This process is more complicated where there are tenants or multiple titles involving private land to make the optimum site for housing development," Dr Smith said.
His policy has met hurdles since being announced last year.
Ngati Whatua took legal action against the Government in June, saying the plans to sell off Crown land to private developers appeared to breach its Treaty of Waitangi agreement.
It later agreed to drop its legal challenge after securing an agreement that 40 per cent of construction would be allocated for social or affordable housing.
New residences
• 600 apartments, Manukau Station Rd, Manukau. Construction: 2 years
• 60 townhouse apartments, New North Rd, Mt Albert. Construction: 2 years
• 80 houses, Great North Rd, Waterview. Construction: 18 months