In 2013, its policy topped out at $460,000 for a house in "high demand areas" of Auckland.
Little has said Labour will have to borrow to pay to develop the houses, but would recoup that as the houses were sold.
The homes would be for first-home buyers only, who would be expected to live in them for a certain period.
Restrictions would be in place to prevent people flicking homes on for a quick profit, including possibly foregoing a portion of any profit if they sell within a certain period.
Most would be medium- or high-density homes on redeveloped or Crown-owned land within the city or on greenfields developments on the outskirts. Labour is likely looking at kitset homes in most cases to keep construction costs low.
The promise of 5000 affordable homes a year is on top of Little's promise on Friday for Labour to build at least 1000 state homes a year, a "high proportion" of which will be in Auckland. That would be paid for by foregoing the dividend from Housing NZ.
He said the Crown already had land set aside for housing.
Little also announced Labour would make Housing NZ a ministry instead of a corporation and the dividends it paid to the Government would instead be used to buy and improve state housing.
Labour will pit its affordable housing policy against National's, which has promised to set aside 20 per cent of the homes on new developments on Crown-owned land for affordable housing and 20 per cent for social housing.
National also last week announced a $1 billion fund to fast-track infrastructure development.
Little said the policy package would also try to slow down property speculation.
Little has ruled out campaigning on a capital gains tax, but there is speculation Labour will expand the "bright line" test from two years out to three-five years.
That concerned Andrew King of the Property Investors Federation, who said it would punish genuine longer term rental property investors rather than speculators.
"Any increase in the term would change the focus of the test to rental property providers. Ultimately this would have a flow-on and negative effect for tenants, which Labour would obviously want to avoid."
Another option is to remove negative gearing, which allows landlords to claim tax deductions on any loss if their rental earns less than it costs in mortgage interest and maintenance.